IODS course project
Abushahba
About the project
This seems very interesting course, I am much excited day after day about its potentials and applications!
My Github repository is here
Regression and model validation
Here we practice Data management and wrangling as well as linear Regression model creation and analysis.
Our data set from Data wrangling will be used, R script for Data wrangling can be found here
Reading students2014 data, Explore the structure and the dimensions of the data
read.csv (file = "C:/Users/ahmed/Desktop/IODS-project/data/learning2014_AGA.csv")## X gender Age Attitude deep stra surf Points
## 1 1 F 53 37 3.583333 3.375 2.583333 25
## 2 2 M 55 31 2.916667 2.750 3.166667 12
## 3 3 F 49 25 3.500000 3.625 2.250000 24
## 4 4 M 53 35 3.500000 3.125 2.250000 10
## 5 5 M 49 37 3.666667 3.625 2.833333 22
## 6 6 F 38 38 4.750000 3.625 2.416667 21
## 7 7 M 50 35 3.833333 2.250 1.916667 21
## 8 8 F 37 29 3.250000 4.000 2.833333 31
## 9 9 M 37 38 4.333333 4.250 2.166667 24
## 10 10 F 42 21 4.000000 3.500 3.000000 26
## 11 11 M 37 39 3.583333 3.625 2.666667 31
## 12 12 F 34 38 3.833333 4.750 2.416667 31
## 13 13 F 34 24 4.250000 3.625 2.250000 23
## 14 14 F 34 30 3.333333 3.500 2.750000 25
## 15 15 M 35 26 4.166667 1.750 2.333333 21
## 16 16 F 33 41 3.666667 3.875 2.333333 31
## 17 17 F 32 26 4.083333 1.375 2.916667 20
## 18 18 F 44 26 3.500000 3.250 2.500000 22
## 19 19 M 29 17 4.083333 3.000 3.750000 9
## 20 20 F 30 27 4.000000 3.750 2.750000 24
## 21 21 M 27 39 3.916667 2.625 2.333333 28
## 22 22 M 29 34 4.000000 2.375 2.416667 30
## 23 23 F 31 27 4.000000 3.625 3.000000 24
## 24 24 F 37 23 3.666667 2.750 2.416667 9
## 25 25 F 26 37 3.666667 1.750 2.833333 26
## 26 26 F 26 44 4.416667 3.250 3.166667 32
## 27 27 M 30 41 3.916667 4.000 3.000000 32
## 28 28 F 33 37 3.750000 3.625 2.000000 33
## 29 29 F 33 25 3.250000 2.875 3.500000 29
## 30 30 M 28 30 3.583333 3.000 3.750000 30
## 31 31 M 26 34 4.916667 1.625 2.500000 19
## 32 32 F 27 32 3.583333 3.250 2.083333 23
## 33 33 F 25 20 2.916667 3.500 2.416667 19
## 34 34 F 31 24 3.666667 3.000 2.583333 12
## 35 35 M 20 42 4.500000 3.250 1.583333 10
## 36 36 F 39 16 4.083333 1.875 2.833333 11
## 37 37 M 38 31 3.833333 4.375 1.833333 20
## 38 38 M 24 38 3.250000 3.625 2.416667 26
## 39 39 M 26 38 2.333333 2.500 3.250000 31
## 40 40 M 25 33 3.333333 1.250 3.416667 20
## 41 41 F 30 17 4.083333 4.000 3.416667 23
## 42 42 F 25 25 2.916667 3.000 3.166667 12
## 43 43 M 30 32 3.333333 2.500 3.500000 24
## 44 44 F 48 35 3.833333 4.875 2.666667 17
## 45 45 F 24 32 3.666667 5.000 2.416667 29
## 46 46 F 40 42 4.666667 4.375 3.583333 23
## 47 47 M 25 31 3.750000 3.250 2.083333 28
## 48 48 F 23 39 3.416667 4.000 3.750000 31
## 49 49 F 25 19 4.166667 3.125 2.916667 23
## 50 50 F 23 21 2.916667 2.500 2.916667 25
## 51 51 M 27 25 4.166667 3.125 2.416667 18
## 52 52 M 25 32 3.583333 3.250 3.000000 19
## 53 53 M 23 32 2.833333 2.125 3.416667 22
## 54 54 F 23 26 4.000000 2.750 2.916667 25
## 55 55 F 23 23 2.916667 2.375 3.250000 21
## 56 56 F 45 38 3.000000 3.125 3.250000 9
## 57 57 F 22 28 4.083333 4.000 2.333333 28
## 58 58 F 23 33 2.916667 4.000 3.250000 25
## 59 59 M 21 48 3.500000 2.250 2.500000 29
## 60 60 M 21 40 4.333333 3.250 1.750000 33
## 61 61 F 21 40 4.250000 3.625 2.250000 33
## 62 62 F 21 47 3.416667 3.625 2.083333 25
## 63 63 F 26 23 3.083333 2.500 2.833333 18
## 64 64 F 25 31 4.583333 1.875 2.833333 22
## 65 65 F 26 27 3.416667 2.000 2.416667 17
## 66 66 M 21 41 3.416667 1.875 2.250000 25
## 67 67 F 23 34 3.416667 4.000 2.833333 28
## 68 68 F 22 25 3.583333 2.875 2.250000 22
## 69 69 F 22 21 1.583333 3.875 1.833333 26
## 70 70 F 22 14 3.333333 2.500 2.916667 11
## 71 71 F 23 19 4.333333 2.750 2.916667 29
## 72 72 M 22 37 4.416667 4.500 2.083333 22
## 73 73 M 23 32 4.833333 3.375 2.333333 21
## 74 74 M 24 28 3.083333 2.625 2.416667 28
## 75 75 F 22 41 3.000000 4.125 2.750000 33
## 76 76 F 23 25 4.083333 2.625 3.250000 16
## 77 77 M 22 28 4.083333 2.250 1.750000 31
## 78 78 M 20 38 3.750000 2.750 2.583333 22
## 79 79 M 22 31 3.083333 3.000 3.333333 31
## 80 80 M 21 35 4.750000 1.625 2.833333 23
## 81 81 F 22 36 4.250000 1.875 2.500000 26
## 82 82 F 23 26 4.166667 3.375 2.416667 12
## 83 83 M 21 44 4.416667 3.750 2.416667 26
## 84 84 M 22 45 3.833333 2.125 2.583333 31
## 85 85 M 29 32 3.333333 2.375 3.000000 19
## 86 86 F 29 39 3.166667 2.750 2.000000 30
## 87 87 F 21 25 3.166667 3.125 3.416667 12
## 88 88 M 28 33 3.833333 3.500 2.833333 17
## 89 89 F 21 33 4.250000 2.625 2.250000 18
## 90 90 F 30 30 3.833333 3.375 2.750000 19
## 91 91 F 21 29 3.666667 2.250 3.916667 21
## 92 92 M 23 33 3.833333 3.000 2.333333 24
## 93 93 F 21 33 3.833333 4.000 2.750000 28
## 94 94 F 21 35 3.833333 3.500 2.750000 17
## 95 95 F 20 36 3.666667 2.625 2.916667 18
## 96 96 M 22 37 4.333333 2.500 2.083333 17
## 97 97 M 21 42 3.750000 3.750 3.666667 23
## 98 98 M 21 32 4.166667 3.625 2.833333 26
## 99 99 F 20 50 4.000000 4.125 3.416667 28
## 100 100 M 22 47 4.000000 4.375 1.583333 31
## 101 101 F 20 36 4.583333 2.625 2.916667 27
## 102 102 F 20 36 3.666667 4.000 3.000000 25
## 103 103 M 24 29 3.666667 2.750 2.916667 23
## 104 104 F 20 35 3.833333 2.750 2.666667 21
## 105 105 F 19 40 2.583333 1.375 3.000000 27
## 106 106 F 21 35 3.500000 2.250 2.750000 28
## 107 107 F 21 32 3.083333 3.625 3.083333 23
## 108 108 F 22 26 4.250000 3.750 2.500000 21
## 109 109 F 25 20 3.166667 4.000 2.333333 25
## 110 110 F 21 27 3.083333 3.125 3.000000 11
## 111 111 F 22 32 4.166667 3.250 3.000000 19
## 112 112 F 25 33 2.250000 2.125 4.000000 24
## 113 113 F 20 39 3.333333 2.875 3.250000 28
## 114 114 M 24 33 3.083333 1.500 3.500000 21
## 115 115 F 20 30 2.750000 2.500 3.500000 24
## 116 116 M 21 37 3.250000 3.250 3.833333 24
## 117 117 F 20 25 4.000000 3.625 2.916667 20
## 118 118 F 20 29 3.583333 3.875 2.166667 19
## 119 119 M 31 39 4.083333 3.875 1.666667 30
## 120 120 F 20 36 4.250000 2.375 2.083333 22
## 121 121 F 22 29 3.416667 3.000 2.833333 16
## 122 122 F 22 21 3.083333 3.375 3.416667 16
## 123 123 M 21 31 3.500000 2.750 3.333333 19
## 124 124 M 22 40 3.666667 4.500 2.583333 30
## 125 125 F 21 31 4.250000 2.625 2.833333 23
## 126 126 F 21 23 4.250000 2.750 3.333333 19
## 127 127 F 21 28 3.833333 3.250 3.000000 18
## 128 128 F 21 37 4.416667 4.125 2.583333 28
## 129 129 F 20 26 3.500000 3.375 2.416667 21
## 130 130 F 21 24 3.583333 2.750 3.583333 19
## 131 131 F 25 30 3.666667 4.125 2.083333 27
## 132 132 M 21 28 2.083333 3.250 4.333333 24
## 133 133 F 24 29 4.250000 2.875 2.666667 21
## 134 134 F 20 24 3.583333 2.875 3.000000 20
## 135 135 M 21 31 4.000000 2.375 2.666667 28
## 136 136 F 20 19 3.333333 3.875 2.166667 12
## 137 137 F 20 20 3.500000 2.125 2.666667 21
## 138 138 F 18 38 3.166667 4.000 2.250000 28
## 139 139 F 21 34 3.583333 3.250 2.666667 31
## 140 140 F 19 37 3.416667 2.625 3.333333 18
## 141 141 F 21 29 4.250000 2.750 3.500000 25
## 142 142 F 20 23 3.250000 4.000 2.750000 19
## 143 143 M 21 41 4.416667 3.000 2.000000 21
## 144 144 F 20 27 3.250000 3.375 2.833333 16
## 145 145 F 21 35 3.916667 3.875 3.500000 7
## 146 146 F 20 34 3.583333 3.250 2.500000 21
## 147 147 F 18 32 4.500000 3.375 3.166667 17
## 148 148 M 22 33 3.583333 4.125 3.083333 22
## 149 149 F 22 33 3.666667 3.500 2.916667 18
## 150 150 M 24 35 2.583333 2.000 3.166667 25
## 151 151 F 19 32 4.166667 3.625 2.500000 24
## 152 152 F 20 31 3.250000 3.375 3.833333 23
## 153 153 F 20 28 4.333333 2.125 2.250000 23
## 154 154 F 17 17 3.916667 4.625 3.416667 26
## 155 155 M 19 19 2.666667 2.500 3.750000 12
## 156 156 F 20 35 3.083333 2.875 3.000000 32
## 157 157 F 20 24 3.750000 2.750 2.583333 22
## 158 158 F 20 21 4.166667 4.000 3.333333 20
## 159 159 F 20 29 4.166667 2.375 2.833333 21
## 160 160 F 19 19 3.250000 3.875 3.000000 23
## 161 161 F 19 20 4.083333 3.375 2.833333 20
## 162 162 F 22 42 2.916667 1.750 3.166667 28
## 163 163 M 35 41 3.833333 3.000 2.750000 31
## 164 164 F 18 37 3.166667 2.625 3.416667 18
## 165 165 F 19 36 3.416667 2.625 3.000000 30
## 166 166 M 21 18 4.083333 3.375 2.666667 19let’s make it in “lrn2014_AGA”
lrn2014_AGA <- read.csv (file = "C:/Users/ahmed/Desktop/IODS-project/data/learning2014_AGA.csv")
str(lrn2014_AGA)## 'data.frame': 166 obs. of 8 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ gender : Factor w/ 2 levels "F","M": 1 2 1 2 2 1 2 1 2 1 ...
## $ Age : int 53 55 49 53 49 38 50 37 37 42 ...
## $ Attitude: int 37 31 25 35 37 38 35 29 38 21 ...
## $ deep : num 3.58 2.92 3.5 3.5 3.67 ...
## $ stra : num 3.38 2.75 3.62 3.12 3.62 ...
## $ surf : num 2.58 3.17 2.25 2.25 2.83 ...
## $ Points : int 25 12 24 10 22 21 21 31 24 26 ...dim(lrn2014_AGA)## [1] 166 8structure shows that we have data frame of 166 observations about 8 variables describing students’ performance.
Graphical overview of the data
now let’s have a graphical overview of the data, can we access ggplot2 and GGally library? NO! we need to install package first!
library(ggplot2)
library(GGally)
plot <- ggpairs(lrn2014_AGA, mapping = aes(col = gender, alpha = 0.3), lower = list(combo = wrap("facethist", bins = 20)))
plot
looking onto our plots we can have an idea about normality of distribution, different variables correlation, Our sample included more females almost double males, We can see for example that Age is more correlated with strategic thinking, then with Attitude and deep thinking almost similarily, while it is not correlated Points and superficial thinking.The attitude is relatively highly correlated with the Points earned, however, it’s also correlated to deep thinking more than with strategic thinking. Deep thinking is somehow correlated with strategic thinking.Strategic thinking has somthing to do with Points Whereas superficial thinking is not correlated with Points.
summary(lrn2014_AGA)## X gender Age Attitude deep
## Min. : 1.00 F:110 Min. :17.00 Min. :14.00 Min. :1.583
## 1st Qu.: 42.25 M: 56 1st Qu.:21.00 1st Qu.:26.00 1st Qu.:3.333
## Median : 83.50 Median :22.00 Median :32.00 Median :3.667
## Mean : 83.50 Mean :25.51 Mean :31.43 Mean :3.680
## 3rd Qu.:124.75 3rd Qu.:27.00 3rd Qu.:37.00 3rd Qu.:4.083
## Max. :166.00 Max. :55.00 Max. :50.00 Max. :4.917
## stra surf Points
## Min. :1.250 Min. :1.583 Min. : 7.00
## 1st Qu.:2.625 1st Qu.:2.417 1st Qu.:19.00
## Median :3.188 Median :2.833 Median :23.00
## Mean :3.121 Mean :2.787 Mean :22.72
## 3rd Qu.:3.625 3rd Qu.:3.167 3rd Qu.:27.75
## Max. :5.000 Max. :4.333 Max. :33.00Regression Model fitting
Now let’s hypthesize a model to test how Attitude, deep and strategic thinking affect student’s exam points
fit <- lm(Points ~ Attitude + deep + stra, data = lrn2014_AGA)
summary(fit)##
## Call:
## lm(formula = Points ~ Attitude + deep + stra, data = lrn2014_AGA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.5239 -3.4276 0.5474 3.8220 11.5112
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.39145 3.40775 3.343 0.00103 **
## Attitude 0.35254 0.05683 6.203 4.44e-09 ***
## deep -0.74920 0.75066 -0.998 0.31974
## stra 0.96208 0.53668 1.793 0.07489 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.289 on 162 degrees of freedom
## Multiple R-squared: 0.2097, Adjusted R-squared: 0.195
## F-statistic: 14.33 on 3 and 162 DF, p-value: 2.521e-08Summary showing in the coefficients section that there is higher probability that deep thinking values are wrong, so it should be rejected from our model.Now let’s return back to our fit model and try to refine by backwards elimination
fit <- lm(Points ~ Attitude + stra, data = lrn2014_AGA)
summary(fit)##
## Call:
## lm(formula = Points ~ Attitude + stra, data = lrn2014_AGA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.6436 -3.3113 0.5575 3.7928 10.9295
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.97290 2.39591 3.745 0.00025 ***
## Attitude 0.34658 0.05652 6.132 6.31e-09 ***
## stra 0.91365 0.53447 1.709 0.08927 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.289 on 163 degrees of freedom
## Multiple R-squared: 0.2048, Adjusted R-squared: 0.1951
## F-statistic: 20.99 on 2 and 163 DF, p-value: 7.734e-09I am still not convinced to keep strategic thinking, let’s trim it!
fit <- lm(Points ~ Attitude , data = lrn2014_AGA)
summary(fit)##
## Call:
## lm(formula = Points ~ Attitude, data = lrn2014_AGA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.9763 -3.2119 0.4339 4.1534 10.6645
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.63715 1.83035 6.358 1.95e-09 ***
## Attitude 0.35255 0.05674 6.214 4.12e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.32 on 164 degrees of freedom
## Multiple R-squared: 0.1906, Adjusted R-squared: 0.1856
## F-statistic: 38.61 on 1 and 164 DF, p-value: 4.119e-09According to this we can conclude that there is some statistical relationship between Student attitude and his exam points. what about the low R-squared? is it always bad? please see: http://blog.minitab.com/blog/adventures-in-statistics-2/regression-analysis-how-do-i-interpret-r-squared-and-assess-the-goodness-of-fit
Model Analysis
let’s have alook on the distribution and variability of the data around the regression line using some diagnostic plots
plot(fit, which = c(1, 2, 5))
The low R-squared graph shows that even noisy, high-variability data can have a significant trend.The trend indicates that the predictor variable still provides information about the response even though data points fall further from the regression line.
we assume that errors are normally distributed, right? well look at the QQ-plot you will find that most of the points fit to the underlying line (more or less), so our assumption of normal distribution for the errors is ok! next plot shows how the residuals are reasonably random spread around our model, which is good hopefully, as it tells that size of errors shold not depend on explanatory variables. Final plot; residuals vs. leverage, showing that although we have some outliers but they are more or less equally distributed exerting regular leverage, that I feel that we don’t need to worry about!
Logistic regression
Here we will practice some priciples of logistic regression using the joined student alcohol consumption data, let’s have a look on that
analys3 <-read.csv("C:/Users/ahmed/Desktop/IODS-project/data/joined data set for analysis.csv")
glimpse(analys3)## Observations: 382
## Variables: 36
## $ X <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
## $ ï..school <fctr> GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP, GP...
## $ sex <fctr> F, F, F, F, F, M, M, F, M, M, F, F, M, M, M, F, F,...
## $ age <int> 18, 17, 15, 15, 16, 16, 16, 17, 15, 15, 15, 15, 15,...
## $ address <fctr> U, U, U, U, U, U, U, U, U, U, U, U, U, U, U, U, U,...
## $ famsize <fctr> GT3, GT3, LE3, GT3, GT3, LE3, LE3, GT3, LE3, GT3, ...
## $ Pstatus <fctr> A, T, T, T, T, T, T, A, A, T, T, T, T, T, A, T, T,...
## $ Medu <int> 4, 1, 1, 4, 3, 4, 2, 4, 3, 3, 4, 2, 4, 4, 2, 4, 4, ...
## $ Fedu <int> 4, 1, 1, 2, 3, 3, 2, 4, 2, 4, 4, 1, 4, 3, 2, 4, 4, ...
## $ Mjob <fctr> at_home, at_home, at_home, health, other, services...
## $ Fjob <fctr> teacher, other, other, services, other, other, oth...
## $ reason <fctr> course, course, other, home, home, reputation, hom...
## $ nursery <fctr> yes, no, yes, yes, yes, yes, yes, yes, yes, yes, y...
## $ internet <fctr> no, yes, yes, yes, no, yes, yes, no, yes, yes, yes...
## $ guardian <fctr> mother, father, mother, mother, father, mother, mo...
## $ traveltime <int> 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, ...
## $ studytime <int> 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 3, 1, 3, ...
## $ failures <int> 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ schoolsup <fctr> yes, no, yes, no, no, no, no, yes, no, no, no, no,...
## $ famsup <fctr> no, yes, no, yes, yes, yes, no, yes, yes, yes, yes...
## $ paid <fctr> no, no, yes, yes, yes, yes, no, no, yes, yes, yes,...
## $ activities <fctr> no, no, no, yes, no, yes, no, no, no, yes, no, yes...
## $ higher <fctr> yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, ...
## $ romantic <fctr> no, no, no, yes, no, no, no, no, no, no, no, no, n...
## $ famrel <int> 4, 5, 4, 3, 4, 5, 4, 4, 4, 5, 3, 5, 4, 5, 4, 4, 3, ...
## $ freetime <int> 3, 3, 3, 2, 3, 4, 4, 1, 2, 5, 3, 2, 3, 4, 5, 4, 2, ...
## $ goout <int> 4, 3, 2, 2, 2, 2, 4, 4, 2, 1, 3, 2, 3, 3, 2, 4, 3, ...
## $ Dalc <int> 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
## $ Walc <int> 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1, 3, 2, 1, 2, 2, ...
## $ health <int> 3, 3, 3, 5, 5, 5, 3, 1, 1, 5, 2, 4, 5, 3, 3, 2, 2, ...
## $ absences <int> 5, 3, 8, 1, 2, 8, 0, 4, 0, 0, 1, 2, 1, 1, 0, 5, 8, ...
## $ G1 <int> 2, 7, 10, 14, 8, 14, 12, 8, 16, 13, 12, 10, 13, 11,...
## $ G2 <int> 8, 8, 10, 14, 12, 14, 12, 9, 17, 14, 11, 12, 14, 11...
## $ G3 <int> 8, 8, 11, 14, 12, 14, 12, 10, 18, 14, 12, 12, 13, 1...
## $ alc_use <dbl> 1.0, 1.0, 2.5, 1.0, 1.5, 1.5, 1.0, 1.0, 1.0, 1.0, 1...
## $ high_use <lgl> FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, FAL...This data approach student achievement in secondary education of two Portuguese schools. The data (in the two sets) attributes include student grades, demographic, social and school related features and it was collected by using school reports and questionnaires, more details can be found here, I have performed some data wrangling to Keep only the students present in both data sets, combine the ‘duplicated’ answers in the joined data, take the average of the answers related to weekday and weekend alcohol consumption and create a new logical column ‘high_use’ which is TRUE for students for which ‘alc_use’ is greater than 2 (and FALSE otherwise), and the Rscript for that can be found here
The purpose
The purpose of analysis is to study the relationships between high/low alcohol consumption and some of the other variables in the data. To do this, we choose 4 interesting variables in the data; absences,quality of family relationship, sex (M) and free time after school. We hypthesize that those factors are correlated with higher alchol consumption.
Let’s have a look on that:
g1 <- ggplot(analys3, aes(x = high_use, y = absences, col = sex))
g1 + geom_boxplot()
g2 <- ggplot(analys3, aes(x = high_use, y = famrel, col = sex))
g2 + geom_boxplot()
g3 <- ggplot(analys3, aes(x = high_use, y = freetime, col = sex))
g3 + geom_boxplot()
analys3 %>% group_by(sex, absences, famrel, high_use) %>% summarise(count = n(), mean_freetime = mean(freetime))## # A tibble: 149 x 6
## # Groups: sex, absences, famrel [?]
## sex absences famrel high_use count mean_freetime
## <fctr> <int> <int> <lgl> <int> <dbl>
## 1 F 0 3 FALSE 2 2.500000
## 2 F 0 3 TRUE 3 3.333333
## 3 F 0 4 FALSE 15 2.933333
## 4 F 0 4 TRUE 2 3.500000
## 5 F 0 5 FALSE 11 2.636364
## 6 F 0 5 TRUE 1 4.000000
## 7 F 1 1 FALSE 1 2.000000
## 8 F 1 2 FALSE 1 3.000000
## 9 F 1 2 TRUE 1 3.000000
## 10 F 1 3 FALSE 6 3.000000
## # ... with 139 more rowsAccording to previous summaries; high_use is more related with higher absences espicially for males, weaker family relationship status equally for males and females and unlikely to be correlated with freetime espicially for males.
Fitting a model
To statistically test this lets fit logistic regression to explore the relationship between our chosen variables and the binary high/low alcohol consumption variable as the target variable.
m <- glm(high_use ~ absences + sex + famrel + freetime, data = analys3, family = "binomial")
summary(m)##
## Call:
## glm(formula = high_use ~ absences + sex + famrel + freetime,
## family = "binomial", data = analys3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9125 -0.8195 -0.5923 1.0419 2.0860
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.56113 0.62549 -2.496 0.012565 *
## absences 0.09488 0.02244 4.229 2.35e-05 ***
## sexM 0.92271 0.24859 3.712 0.000206 ***
## famrel -0.34855 0.13181 -2.644 0.008187 **
## freetime 0.33967 0.12673 2.680 0.007358 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 465.68 on 381 degrees of freedom
## Residual deviance: 417.44 on 377 degrees of freedom
## AIC: 427.44
##
## Number of Fisher Scoring iterations: 4so, in the summary of our model we can taste the close correlation between absences, sex variables and higher use of alchol, and less correlation yet present between status of family relatoiship and freetime with higher alchol consumption.
let’s print out the coefficients of the model to use to obtain Odds ratio (OR) and then confidence intervals (CI)
coef(m)## (Intercept) absences sexM famrel freetime
## -1.56112511 0.09487753 0.92270514 -0.34854597 0.33967147OR <- coef(m) %>% exp()
CI <- confint(m) %>% exp()## Waiting for profiling to be done...cbind(OR, CI)## OR 2.5 % 97.5 %
## (Intercept) 0.2098998 0.0600191 0.7022687
## absences 1.0995242 1.0542744 1.1516588
## sexM 2.5160876 1.5542543 4.1270709
## famrel 0.7057135 0.5433500 0.9127012
## freetime 1.4044861 1.0989755 1.8082673Based on that we can see that family relation status is less likely to correlate with higher alchol consumption (contradicting our initial hypothesis) as it shows less than 1 OR with a CI crossing line at 1, followed by absences, then with more likelihood of correlation follws freetime (again challenging our initial hypothesis) and SexM variables. So, I would conclude that higher alchol consumption is much correlated with SexM and freetime.
Exploring the predictive power of our model
m <- glm(high_use ~ freetime + absences + sex, data = analys3, family = "binomial")
probabilities <- predict(m, type = "response")
analys3 <- mutate(analys3, probability = probabilities)
analys3 <- mutate(analys3, prediction = (probability > 0.5))
select(analys3, freetime, absences, sex, high_use, probability, prediction) %>% tail(10)## freetime absences sex high_use probability prediction
## 373 3 0 M FALSE 0.2696155 FALSE
## 374 4 7 M TRUE 0.4945212 FALSE
## 375 3 1 F FALSE 0.1449414 FALSE
## 376 4 6 F FALSE 0.2697703 FALSE
## 377 4 2 F FALSE 0.1998871 FALSE
## 378 3 2 F FALSE 0.1574882 FALSE
## 379 2 2 F FALSE 0.1227034 FALSE
## 380 1 3 F FALSE 0.1034644 FALSE
## 381 4 4 M TRUE 0.4218155 FALSE
## 382 4 2 M TRUE 0.3749754 FALSEtable(high_use = analys3$high_use, prediction = analys3$prediction) %>% prop.table() %>% addmargins()## prediction
## high_use FALSE TRUE Sum
## FALSE 0.66492147 0.03664921 0.70157068
## TRUE 0.23036649 0.06806283 0.29842932
## Sum 0.89528796 0.10471204 1.00000000g <- ggplot(analys3, aes(x = probability, y = high_use, col = prediction))
g + geom_point()
It is evident that our prediction is not sensitive enough to predict higher alchol consumption; however, it was relatively specific in prdicting lower alchol consumers.
Now, let’s compute the total proportion of inaccurately classified individuals
loss_func <- function(class, prob) {
n_wrong <- abs(class - prob) > 0.5
mean(n_wrong)
}
loss_func(class = analys3$high_use, prob = analys3$probability)## [1] 0.2670157so, in our model the mean of incorrectly classified observations is around 0.267
Cross validation
Performing 10-fold cross-validation on our model, compute the average number of wrong predictions in the (training) data, compare to average number of wrong predictions in the cross validation
loss_func <- function(class, prob) {
n_wrong <- abs(class - prob) > 0.5
mean(n_wrong)
}
loss_func(class = analys3$high_use, prob = analys3$probability)## [1] 0.2670157library(boot)
cv <- cv.glm(data = analys3, cost = loss_func, glmfit = m, K = 10)
cv$delta[1]## [1] 0.2748691prediction error higher on the testing data compared to the training data.
Clustering and classification
Analysis exercises
We will work on the Boston data from the MASS package which comprises Housing Values in Suburbs of Boston, let’s load and explore it.
library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## selectEx4 <- Boston
str(Ex4)## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ black : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...Our data frame(Boston) has 506 obseravations of 14 variables which are all numerical except for two integers (Charles River dummy variable (= 1 if tract bounds river; 0 otherwise and index of accessibility to radial highways).
It is nice to have some graphical overview of the data as follows:
summary(Ex4)## crim zn indus chas
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000
## 1st Qu.: 0.08204 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000
## nox rm age dis
## Min. :0.3850 Min. :3.561 Min. : 2.90 Min. : 1.130
## 1st Qu.:0.4490 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100
## Median :0.5380 Median :6.208 Median : 77.50 Median : 3.207
## Mean :0.5547 Mean :6.285 Mean : 68.57 Mean : 3.795
## 3rd Qu.:0.6240 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188
## Max. :0.8710 Max. :8.780 Max. :100.00 Max. :12.127
## rad tax ptratio black
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 0.32
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.:375.38
## Median : 5.000 Median :330.0 Median :19.05 Median :391.44
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :356.67
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:396.23
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :396.90
## lstat medv
## Min. : 1.73 Min. : 5.00
## 1st Qu.: 6.95 1st Qu.:17.02
## Median :11.36 Median :21.20
## Mean :12.65 Mean :22.53
## 3rd Qu.:16.95 3rd Qu.:25.00
## Max. :37.97 Max. :50.00library(ggplot2)
library(GGally)
plot1 <- ggpairs(Ex4,
upper = list(continuous = wrap("cor", size = 3)),
lower = list(continuous = wrap("points", alpha = .2, size = .6),
combo = wrap("facethist", bins = 10))) +
theme(
axis.text.x = element_text(angle = 90, color = "black", size = 7, vjust = .5),
axis.text.y = element_text(color = "black", size = 7))
plot1
Can we have better visualization for the correlation? I think corrplot() function (from the corrplot package) could help, let’s see!
library(corrplot)## corrplot 0.84 loadedlibrary(tidyverse)## -- Attaching packages -------------------------------------------------------------------------- tidyverse 1.2.1 --## v tibble 1.3.4 v purrr 0.2.4
## v tidyr 0.7.2 v stringr 1.2.0
## v readr 1.1.1 v forcats 0.2.0## -- Conflicts ----------------------------------------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
## x MASS::select() masks dplyr::select()cor_matrix<-cor(Ex4) %>% round(2)
cor_matrix## crim zn indus chas nox rm age dis rad tax
## crim 1.00 -0.20 0.41 -0.06 0.42 -0.22 0.35 -0.38 0.63 0.58
## zn -0.20 1.00 -0.53 -0.04 -0.52 0.31 -0.57 0.66 -0.31 -0.31
## indus 0.41 -0.53 1.00 0.06 0.76 -0.39 0.64 -0.71 0.60 0.72
## chas -0.06 -0.04 0.06 1.00 0.09 0.09 0.09 -0.10 -0.01 -0.04
## nox 0.42 -0.52 0.76 0.09 1.00 -0.30 0.73 -0.77 0.61 0.67
## rm -0.22 0.31 -0.39 0.09 -0.30 1.00 -0.24 0.21 -0.21 -0.29
## age 0.35 -0.57 0.64 0.09 0.73 -0.24 1.00 -0.75 0.46 0.51
## dis -0.38 0.66 -0.71 -0.10 -0.77 0.21 -0.75 1.00 -0.49 -0.53
## rad 0.63 -0.31 0.60 -0.01 0.61 -0.21 0.46 -0.49 1.00 0.91
## tax 0.58 -0.31 0.72 -0.04 0.67 -0.29 0.51 -0.53 0.91 1.00
## ptratio 0.29 -0.39 0.38 -0.12 0.19 -0.36 0.26 -0.23 0.46 0.46
## black -0.39 0.18 -0.36 0.05 -0.38 0.13 -0.27 0.29 -0.44 -0.44
## lstat 0.46 -0.41 0.60 -0.05 0.59 -0.61 0.60 -0.50 0.49 0.54
## medv -0.39 0.36 -0.48 0.18 -0.43 0.70 -0.38 0.25 -0.38 -0.47
## ptratio black lstat medv
## crim 0.29 -0.39 0.46 -0.39
## zn -0.39 0.18 -0.41 0.36
## indus 0.38 -0.36 0.60 -0.48
## chas -0.12 0.05 -0.05 0.18
## nox 0.19 -0.38 0.59 -0.43
## rm -0.36 0.13 -0.61 0.70
## age 0.26 -0.27 0.60 -0.38
## dis -0.23 0.29 -0.50 0.25
## rad 0.46 -0.44 0.49 -0.38
## tax 0.46 -0.44 0.54 -0.47
## ptratio 1.00 -0.18 0.37 -0.51
## black -0.18 1.00 -0.37 0.33
## lstat 0.37 -0.37 1.00 -0.74
## medv -0.51 0.33 -0.74 1.00corrplot(cor_matrix, method="circle", type = "upper", cl.pos = "b", tl.pos = "d", tl.cex = 0.6)
So, now we can rather easily interpret or taste the correlation pattern between many variables. We can say for example that crim shows relatively more correlation with rad and proportion of non-retail business acres per town is highly correlated with nitrogen oxides concentration (parts per 10 million). Same for correlation between rad and tax and the negative correlation between age and dis. However, the current data state is a bit diverse and unscaled that hinders true interpretations; which should be dealt with next.
Ex4_scaled <- scale(Ex4)
summary(Ex4_scaled)## crim zn indus
## Min. :-0.419367 Min. :-0.48724 Min. :-1.5563
## 1st Qu.:-0.410563 1st Qu.:-0.48724 1st Qu.:-0.8668
## Median :-0.390280 Median :-0.48724 Median :-0.2109
## Mean : 0.000000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.007389 3rd Qu.: 0.04872 3rd Qu.: 1.0150
## Max. : 9.924110 Max. : 3.80047 Max. : 2.4202
## chas nox rm age
## Min. :-0.2723 Min. :-1.4644 Min. :-3.8764 Min. :-2.3331
## 1st Qu.:-0.2723 1st Qu.:-0.9121 1st Qu.:-0.5681 1st Qu.:-0.8366
## Median :-0.2723 Median :-0.1441 Median :-0.1084 Median : 0.3171
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.:-0.2723 3rd Qu.: 0.5981 3rd Qu.: 0.4823 3rd Qu.: 0.9059
## Max. : 3.6648 Max. : 2.7296 Max. : 3.5515 Max. : 1.1164
## dis rad tax ptratio
## Min. :-1.2658 Min. :-0.9819 Min. :-1.3127 Min. :-2.7047
## 1st Qu.:-0.8049 1st Qu.:-0.6373 1st Qu.:-0.7668 1st Qu.:-0.4876
## Median :-0.2790 Median :-0.5225 Median :-0.4642 Median : 0.2746
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.6617 3rd Qu.: 1.6596 3rd Qu.: 1.5294 3rd Qu.: 0.8058
## Max. : 3.9566 Max. : 1.6596 Max. : 1.7964 Max. : 1.6372
## black lstat medv
## Min. :-3.9033 Min. :-1.5296 Min. :-1.9063
## 1st Qu.: 0.2049 1st Qu.:-0.7986 1st Qu.:-0.5989
## Median : 0.3808 Median :-0.1811 Median :-0.1449
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4332 3rd Qu.: 0.6024 3rd Qu.: 0.2683
## Max. : 0.4406 Max. : 3.5453 Max. : 2.9865Ex4_scaled <- as.data.frame(Ex4_scaled)
class(Ex4_scaled)## [1] "data.frame"In the scaled data we can notice that all the means are set to 0.0000. Now, let’s focus on the crime rate varable and try to categorize.
summary(Ex4_scaled$crim)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.419367 -0.410563 -0.390280 0.000000 0.007389 9.924110bins <- quantile(Ex4_scaled$crim)
bins## 0% 25% 50% 75% 100%
## -0.419366929 -0.410563278 -0.390280295 0.007389247 9.924109610crime <- cut(Ex4_scaled$crim, breaks = bins, include.lowest = TRUE, label = c("low", "med_low", "med_high", "high"))
table(crime)## crime
## low med_low med_high high
## 127 126 126 127Ex4_scalednocrim <- dplyr::select(Ex4_scaled, -crim)
Ex4_scaledw <- data.frame(Ex4_scalednocrim, crime)
summary(Ex4_scaledw)## zn indus chas nox
## Min. :-0.48724 Min. :-1.5563 Min. :-0.2723 Min. :-1.4644
## 1st Qu.:-0.48724 1st Qu.:-0.8668 1st Qu.:-0.2723 1st Qu.:-0.9121
## Median :-0.48724 Median :-0.2109 Median :-0.2723 Median :-0.1441
## Mean : 0.00000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.04872 3rd Qu.: 1.0150 3rd Qu.:-0.2723 3rd Qu.: 0.5981
## Max. : 3.80047 Max. : 2.4202 Max. : 3.6648 Max. : 2.7296
## rm age dis rad
## Min. :-3.8764 Min. :-2.3331 Min. :-1.2658 Min. :-0.9819
## 1st Qu.:-0.5681 1st Qu.:-0.8366 1st Qu.:-0.8049 1st Qu.:-0.6373
## Median :-0.1084 Median : 0.3171 Median :-0.2790 Median :-0.5225
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4823 3rd Qu.: 0.9059 3rd Qu.: 0.6617 3rd Qu.: 1.6596
## Max. : 3.5515 Max. : 1.1164 Max. : 3.9566 Max. : 1.6596
## tax ptratio black lstat
## Min. :-1.3127 Min. :-2.7047 Min. :-3.9033 Min. :-1.5296
## 1st Qu.:-0.7668 1st Qu.:-0.4876 1st Qu.: 0.2049 1st Qu.:-0.7986
## Median :-0.4642 Median : 0.2746 Median : 0.3808 Median :-0.1811
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 1.5294 3rd Qu.: 0.8058 3rd Qu.: 0.4332 3rd Qu.: 0.6024
## Max. : 1.7964 Max. : 1.6372 Max. : 0.4406 Max. : 3.5453
## medv crime
## Min. :-1.9063 low :127
## 1st Qu.:-0.5989 med_low :126
## Median :-0.1449 med_high:126
## Mean : 0.0000 high :127
## 3rd Qu.: 0.2683
## Max. : 2.9865boston_scaled <- Ex4_scaledwNow, we need to divide the dataset to train and test sets, so that 80% of the data belongs to the train set.
n <- nrow(boston_scaled)
n## [1] 506# choose randomly 80% of the rows
train_set <- sample(n, size = n * 0.8)
train <- boston_scaled[train_set,]
test <- boston_scaled[-train_set,]Now, let’s fit the linear discriminant analysis on the train set. Use the categorical crime rate as the target variable and all the other variables in the dataset as predictor variables.
lda.fit <- lda(crime ~ ., data = train)
lda.fit## Call:
## lda(crime ~ ., data = train)
##
## Prior probabilities of groups:
## low med_low med_high high
## 0.2326733 0.2623762 0.2524752 0.2524752
##
## Group means:
## zn indus chas nox rm
## low 0.89144221 -0.8729270 -0.14667693 -0.8684264 0.46519641
## med_low -0.05927783 -0.3133379 -0.08661679 -0.5845279 -0.09605925
## med_high -0.37710480 0.2000248 0.30665626 0.3973176 0.19698470
## high -0.48724019 1.0171096 -0.04073494 1.0081713 -0.42413844
## age dis rad tax ptratio
## low -0.9053466 0.8094302 -0.6739843 -0.7690895 -0.38338225
## med_low -0.3561053 0.3896918 -0.5463205 -0.5051313 -0.05789749
## med_high 0.3934475 -0.4020899 -0.3873706 -0.2973215 -0.41555376
## high 0.7948847 -0.8446033 1.6382099 1.5141140 0.78087177
## black lstat medv
## low 0.39220600 -0.80656991 0.56957823
## med_low 0.32414486 -0.15199725 0.02966739
## med_high 0.05326296 -0.08100412 0.23713107
## high -0.83374439 0.88606252 -0.68238258
##
## Coefficients of linear discriminants:
## LD1 LD2 LD3
## zn 0.03711715 0.724599086 -0.953578705
## indus 0.03208902 -0.209561223 0.177101519
## chas -0.07894705 -0.117799740 0.003897276
## nox 0.34409749 -0.686213290 -1.165768627
## rm -0.10008290 -0.136616480 -0.168365469
## age 0.25379228 -0.310644127 0.035889321
## dis -0.10612899 -0.177194337 0.322101487
## rad 3.01551254 0.838620019 -0.248590181
## tax -0.01889099 -0.029666674 0.583153776
## ptratio 0.06038409 0.170634649 -0.182661456
## black -0.11998338 0.005993161 0.127508387
## lstat 0.19623326 -0.139906976 0.442573499
## medv 0.16688460 -0.263384241 -0.117461745
##
## Proportion of trace:
## LD1 LD2 LD3
## 0.9446 0.0419 0.0135str(train)## 'data.frame': 404 obs. of 14 variables:
## $ zn : num -0.487 -0.487 3.372 -0.487 -0.487 ...
## $ indus : num -0.755 1.015 -1.077 1.015 1.015 ...
## $ chas : num -0.272 -0.272 -0.272 -0.272 -0.272 ...
## $ nox : num -0.481 0.365 -1.387 0.218 1.366 ...
## $ rm : num -0.631 -1.608 1.664 0.217 0.188 ...
## $ age : num -0.255 1.116 -1.221 0.228 1.056 ...
## $ dis : num -0.198 -1.047 1.207 -0.427 -0.765 ...
## $ rad : num -0.522 1.66 -0.752 1.66 1.66 ...
## $ tax : num -0.767 1.529 -0.974 1.529 1.529 ...
## $ ptratio: num 0.344 0.806 -1.18 0.806 0.806 ...
## $ black : num 0.229 -1.596 0.325 0.402 -0.575 ...
## $ lstat : num -0.174 1.04 -1.336 0.239 0.932 ...
## $ medv : num -0.2754 -0.6777 2.3341 0.0725 -1.0365 ...
## $ crime : Factor w/ 4 levels "low","med_low",..: 2 4 1 3 4 3 4 2 2 1 ...# the function for lda biplot arrows
lda.arrows <- function(x, myscale = 1, arrow_heads = 0.1, color = "red", tex = 0.75, choices = c(1,2)){
heads <- coef(x)
arrows(x0 = 0, y0 = 0,
x1 = myscale * heads[,choices[1]],
y1 = myscale * heads[,choices[2]], col=color, length = arrow_heads)
text(myscale * heads[,choices], labels = row.names(heads),
cex = tex, col=color, pos=3)
}
# classes as numeric
classes <- as.numeric(train$crime)
# plot results
plot(lda.fit, dimen = 2, col = classes, pch = classes)
lda.arrows(lda.fit, myscale = 1)
Save the crime categories from the test set and then remove the categorical crime variable from the test dataset. Then predict the classes with the LDA model on the test data.
cross tabulate the results
table(correct = correct_classes, predicted = lda.pred$class) %>% addmargins()## predicted
## correct low med_low med_high high Sum
## low 17 14 2 0 33
## med_low 2 16 2 0 20
## med_high 0 11 13 0 24
## high 0 0 0 25 25
## Sum 19 41 17 25 102Out of this eventual table we can say that if we use our model to predict low crime rate based on other variables we are 6X more likely to have correct prediction, 1.78X likely to predict med_low crime rate, almost around 13X likely to predict med_high and high crime rates. Thus it is relatively less reliable in detecting med_low crime rate.
We will now reload the Boston dataset and standardize the dataset then calculate the distances between the observations.
library(MASS)
data('Boston')
Boston_scaled <- scale(Boston) %>% as.data.frame()
class(Boston_scaled)## [1] "data.frame"# euclidean distance matrix
dist_eu <- dist(Boston_scaled)
dist_eu## 1 2 3 4 5 6
## 2 1.9356773
## 3 2.2809294 2.0310282
## 4 2.5741175 2.3335157 1.1821904
## 5 2.6906020 2.3727561 1.0547043 0.5825442
## 6 2.2407228 1.5500088 1.6132814 1.1071450 1.3164896
## 7 1.7841939 1.7596710 2.8618599 3.1442855 3.1914074 2.4808284
## 8 2.7044618 2.3009840 3.3564325 3.8007319 3.6212338 3.1606647
## 9 4.2499491 3.6273509 5.1392781 5.4228501 5.2929937 4.6304102
## 10 2.6004186 2.1461113 3.5717921 3.8424245 3.8066037 3.0860989
## 11 2.9830212 2.4522334 3.9081075 4.2460387 4.1584319 3.5556295
## 12 2.1627378 1.8431989 3.2621150 3.5423466 3.5620670 2.7855722
## 13 2.3474898 2.3961628 3.3166430 3.4200903 3.5255881 2.8556346
## 14 3.1042847 1.9073015 2.9412306 2.8551660 3.0241470 2.1271805
## 15 3.2129096 1.8101805 3.1496767 3.2490143 3.3086129 2.4705351
## 16 3.1719345 2.0479070 3.0855291 2.9710555 3.1648969 2.2435735
## 17 3.3095910 2.5650444 2.9988025 2.7105117 3.0036105 2.2790853
## 18 3.4318000 2.0207180 3.4693674 3.5705115 3.5905279 2.7701408
## 19 3.7973987 2.9622022 3.8503720 3.6901047 3.8977688 3.0553380
## 20 3.3255715 2.0972980 3.4242734 3.4452857 3.5636989 2.6395599
## 21 4.2659710 2.9325392 4.5891698 4.7403393 4.7104165 3.8594717
## 22 3.4105035 2.0039904 3.4015256 3.5637858 3.5547817 2.7627571
## 23 3.7788405 2.3778856 3.8884911 4.0706930 4.0220356 3.3022630
## 24 4.0634446 2.6680259 4.2921561 4.4625961 4.4139266 3.6111587
## 25 3.6962449 2.2513336 3.8348011 3.9729878 3.9590156 3.1303024
## 26 3.9665447 2.6598721 4.2214341 4.2775733 4.3247407 3.4086222
## 27 3.6082433 2.1624096 3.7229891 3.8136376 3.8293109 2.9441365
## 28 3.8252920 2.4642364 3.9305380 4.0552749 4.0473891 3.2753819
## 29 3.3285595 1.8813755 3.1381429 3.3590215 3.3116939 2.6876276
## 30 3.1824604 1.8199041 2.7875057 3.0366750 2.9760505 2.4831042
## 31 4.3258853 2.9767731 4.6129108 4.7408021 4.7022799 3.8879968
## 32 3.5818372 2.1638212 3.7143634 3.8936730 3.9016428 3.0804523
## 33 4.9292496 3.7818419 5.1173768 5.2445190 5.1780153 4.5465022
## 34 4.0204095 2.6768335 4.3224722 4.4673378 4.4670051 3.6005772
## 35 4.3294564 3.1040739 4.4925960 4.6891291 4.6425136 3.9617999
## 36 2.4830279 1.4069001 2.8423008 2.9331795 3.0720937 2.1066812
## 37 2.5936826 1.5786261 2.9253572 2.9761888 3.1092033 2.1605166
## 38 2.5740245 1.8307468 2.7704509 2.6169500 2.8714297 1.9172281
## 39 2.7012337 2.1232577 2.6624006 2.4757165 2.7064331 1.9700399
## 40 3.4993032 4.0708979 3.7116599 3.4290812 3.5905877 3.5251675
## 41 3.7922666 4.4494881 3.6967326 3.4303495 3.5661148 3.7791546
## 42 2.9924747 2.8965812 2.3661617 1.9250102 2.3171665 2.2085503
## 43 2.9336977 2.7031301 2.6715097 2.2212323 2.6226032 2.0907834
## 44 2.9369495 2.6562502 2.6971419 2.2684547 2.6358500 2.1149131
## 45 2.3900661 1.5337953 2.4531803 2.2495278 2.5048668 1.5467280
## 46 2.6778910 1.9529768 3.0211046 2.8124352 3.0900845 2.0698176
## 47 2.8102260 2.0048566 3.0920622 2.9313810 3.1247354 2.2248512
## 48 3.0622541 1.6315542 3.4313880 3.5794491 3.5384777 2.6905181
## 49 4.7028207 3.5373350 5.2068233 5.3295644 5.2252596 4.4436889
## 50 2.9721026 1.7575811 3.3295887 3.2663100 3.3451233 2.3278008
## 51 2.4936650 2.0446192 3.1116661 2.9280944 3.0759166 2.2277925
## 52 2.0791770 1.5757458 2.6901255 2.6009107 2.7419825 1.8404145
## 53 2.4146263 2.5727104 2.4579929 2.0521225 2.3882542 1.9947573
## 54 2.5859830 2.5574530 2.9481602 2.5631132 2.8593832 2.1653881
## 55 4.6298697 4.3273594 5.0065158 4.6969228 4.7832378 4.2434683
## 56 4.7273967 5.2266740 4.6017672 4.2256293 4.2710824 4.5269676
## 57 4.1777550 4.6190924 4.6906479 4.2862251 4.4278606 4.1584462
## 58 4.4155816 5.2393243 4.9483590 4.7685487 4.8297108 4.8402925
## 59 3.2860769 2.7922716 3.0908851 2.4572342 2.7472672 2.0903479
## 60 3.0400145 2.2882291 3.1782618 2.7452331 2.9691975 2.0395071
## 61 3.2936427 2.2936753 3.5525063 3.2625584 3.3653647 2.4022463
## 62 3.4010859 2.2309917 3.7337030 3.6559422 3.6608558 2.7762440
## 63 2.8163903 1.9954249 2.6136013 2.3001474 2.4239784 1.7236933
## 64 3.1744072 2.5630626 2.6573790 2.1547315 2.2618960 1.9713783
## 65 3.3794731 2.9493848 2.4668275 1.9332947 1.8085327 2.0643819
## 66 3.6474387 4.3829307 4.4171371 4.1564671 4.3736307 4.0657821
## 67 3.7171177 4.2199602 4.7591759 4.5452751 4.7204783 4.1679546
## 68 3.0846224 2.5656744 3.0776642 2.5953711 2.9221392 2.1101866
## 69 3.2624645 2.4344454 3.5794328 3.2446058 3.4657866 2.4767091
## 70 2.9228067 2.2447243 2.9845109 2.5729165 2.8601352 1.9472170
## 71 3.3837268 2.8244155 2.7501295 2.4689994 2.8067441 2.4291816
## 72 3.3468094 2.5317886 3.0492621 2.8226578 3.1090739 2.4100112
## 73 3.4200337 2.8424595 3.0015060 2.6877540 3.0649907 2.4762976
## 74 3.4319400 2.8342911 2.9221943 2.6342922 2.9687076 2.4897769
## 75 3.3805936 2.9966710 3.0064268 2.9497567 3.2523030 2.8599157
## 76 2.8076761 1.8679317 2.5529415 2.7543275 2.9343858 2.3088156
## 77 2.8722314 1.5606839 2.8004811 3.2184726 3.2519981 2.5883797
## 78 2.8793393 1.9209278 2.7680645 2.9818854 3.1464489 2.4676521
## 79 2.9183146 1.7377377 2.7115576 2.9328498 3.0276882 2.3693539
## 80 3.0514789 2.2051206 3.0288643 3.0941544 3.3280237 2.5512020
## 81 2.4705154 2.3264404 1.9484758 1.5572024 1.8233472 1.6181814
## 82 2.1758072 1.4669939 2.0454744 2.0279384 2.0943464 1.4928276
## 83 2.4879027 2.2053208 2.4046786 2.0003479 2.2941306 1.6662684
## 84 2.3475598 1.8337030 2.4681063 2.1785857 2.4160054 1.5672472
## 85 2.1404592 1.2537716 1.9471894 1.7947334 1.9705159 1.1505053
## 86 1.9687823 1.2366414 1.3808707 1.3976350 1.5528745 0.9598901
## 87 2.4543334 1.5531738 2.5964093 2.4587331 2.6046038 1.7139497
## 88 2.1012124 1.1992518 2.2739958 2.2682829 2.4507657 1.5034576
## 89 1.7940213 1.3973066 1.8020147 2.2974059 2.2717561 1.9720900
## 90 1.7507417 1.7046585 1.1811112 1.6594158 1.6519599 1.6836477
## 91 1.6613999 1.1654026 2.1307367 2.3705038 2.4586685 1.7674920
## 92 1.6736984 1.0897368 2.1958877 2.4795758 2.5518788 1.8328241
## 93 2.5359377 2.0340048 2.5415804 2.9902080 3.1075033 2.6461629
## 94 2.8258088 2.6150966 2.7796490 3.0099654 3.2374862 2.7929480
## 95 2.6788980 1.8536127 2.9362867 3.4539913 3.4903804 2.8815572
## 96 1.8571534 1.5646920 1.5331783 1.7088325 1.7981470 1.4164769
## 97 2.0381368 1.1377793 2.5096289 2.6351695 2.7002620 1.8416765
## 98 3.1850158 3.2245464 1.7340743 2.3598281 2.0371746 2.9583649
## 99 3.4256551 3.6849796 1.8684545 2.1178107 1.9416391 2.9986215
## 100 2.3196220 2.2490727 1.0874949 1.6260237 1.4436884 1.9941256
## 101 3.1407596 2.1921548 2.5009947 2.9059868 2.8297902 2.5892183
## 102 3.0523336 2.1878778 2.3754011 2.7196557 2.7090688 2.4708045
## 103 4.8326550 4.1505539 4.7542712 4.9709743 5.0003479 4.5731192
## 104 3.4245306 2.2237036 3.4500245 3.7264200 3.7165097 3.0453972
## 105 3.4069762 2.2575377 3.4067959 3.7196672 3.7068922 3.0652959
## 106 3.8281565 2.6701490 3.9919246 4.3008813 4.2546827 3.5605182
## 107 3.9161580 2.7512398 4.0799927 4.3649994 4.3084325 3.6276623
## 108 3.4928302 2.3828330 3.5143624 3.8208442 3.8010249 3.1779315
## 109 3.4350778 2.2853511 3.3443649 3.7285992 3.6736671 3.1480383
## 110 3.5642726 2.3613488 3.5788946 3.8970394 3.8437431 3.2382086
## 111 3.2829443 2.3142131 3.1334793 3.2551461 3.3271424 2.7382381
## 112 2.3555199 1.8769599 2.5866643 3.2327741 3.1978701 2.8353248
## 113 3.0830887 2.3458384 3.7565519 4.2422321 4.2088781 3.5196749
## 114 3.0893744 2.3109930 3.7036389 4.2156273 4.1534986 3.5219851
## 115 2.5594785 2.0057712 3.1808777 3.7040886 3.7390044 3.1078168
## 116 3.0456435 2.3338747 3.7167076 4.1786882 4.1680507 3.4668351
## 117 2.4605952 1.8944872 2.9810245 3.4486117 3.4810479 2.8621146
## 118 2.5326913 1.9148506 3.1889751 3.6474199 3.7017146 2.9748462
## 119 2.9188742 2.3141309 3.5330291 3.9430605 3.9640747 3.2764866
## 120 2.7827289 2.2084938 3.4821891 3.8089537 3.8904870 3.1095755
## 121 4.4029357 3.4139841 4.2413621 4.8562654 4.8767944 4.3760794
## 122 4.4306321 3.3807236 4.3000802 4.9719911 4.9661325 4.4660390
## 123 4.6824844 3.5848608 4.5948957 5.2789535 5.2241687 4.7331920
## 124 5.2891453 4.1650569 5.3480280 5.9774262 5.8860480 5.3728732
## 125 4.7354829 3.6320023 4.7217640 5.3917761 5.3505604 4.8131369
## 126 4.4920686 3.4456804 4.3540447 5.0492433 5.0228265 4.5401878
## 127 5.5499021 4.4443398 5.7053200 6.2902971 6.2127633 5.6434520
## 128 5.0151817 3.9565382 5.1070635 5.6134835 5.6016136 4.9919002
## 129 4.7672318 3.7387788 4.6189100 5.2340243 5.1772497 4.7718777
## 130 5.1034678 4.0231762 5.2490412 5.7256325 5.7206537 5.0785141
## 131 4.6139318 3.5994372 4.3931852 5.0152108 4.9725144 4.5791416
## 132 4.5858332 3.5600483 4.3797832 4.9809568 4.9489539 4.5206704
## 133 4.5212885 3.5305628 4.1889816 4.8218647 4.7737840 4.4106886
## 134 4.7739135 3.6879786 4.7418552 5.2563219 5.2430202 4.6679271
## 135 5.1920385 4.1402506 5.2500365 5.7358638 5.7250078 5.1267912
## 136 4.8107227 3.7399587 4.6791911 5.2709994 5.2067465 4.7779650
## 137 4.8704377 3.8091768 4.8591525 5.3921053 5.3665261 4.8264412
## 138 4.7399163 3.7164010 4.6036964 5.2132144 5.1688671 4.7529175
## 139 5.2793628 4.1963117 5.4179383 5.9278103 5.8877062 5.3068433
## 140 4.9593704 3.9049056 4.9099470 5.4879388 5.4258396 4.9580982
## 141 5.3547173 4.2855543 5.4103271 5.9406788 5.8663069 5.3869305
## 142 6.6079306 5.5528070 6.8949806 7.3119504 7.2218157 6.5923332
## 143 6.9463969 6.8317165 7.8089373 8.3212805 8.2751369 7.7901410
## 144 5.6200410 5.4953902 6.5987638 7.2015968 7.1378579 6.6132672
## 145 6.1674025 5.9764380 7.2432254 7.7659028 7.7309011 7.0904979
## 146 6.0792984 5.9712756 6.8968717 7.5156317 7.4353651 7.0377521
## 147 5.5230898 5.5472924 6.4374877 7.0364005 7.0386134 6.5263498
## 148 6.0881274 5.9082764 7.1178963 7.6477169 7.6007346 6.9902733
## 149 5.8053455 5.6678210 6.7618947 7.3278643 7.2653315 6.7225877
## 150 5.1916765 5.1555832 6.1901446 6.8031424 6.7752509 6.2476077
## 151 4.5593474 4.7083083 5.3895160 6.1090882 6.0703544 5.7039894
## 152 4.8551482 4.9445080 5.8364563 6.4677432 6.4773388 5.9299363
## 153 6.3742190 6.4509580 7.2805310 7.7344415 7.7993411 7.2296832
## 154 4.9961689 5.0641703 5.8938659 6.5420279 6.5261584 6.0519308
## 155 6.1263021 6.2038531 6.8435460 7.4112127 7.3965134 7.0428551
## 156 6.9132994 7.0117658 7.5514224 8.0418178 8.0591736 7.7240380
## 157 6.0783486 6.0871870 7.0105876 7.5195864 7.5613748 6.9828639
## 158 3.7869175 4.0086275 3.5161353 4.5722413 4.4183748 4.5882165
## 159 3.3951139 3.3764767 4.0188357 4.8732662 4.8782900 4.4427647
## 160 4.3487259 4.6453381 5.0465499 5.8171366 5.7957322 5.5366866
## 161 5.1323778 5.1840638 5.4484556 6.0964233 6.0973634 5.8481773
## 162 4.4472763 4.7956901 3.7482087 4.7795552 4.5778835 5.0679986
## 163 6.0874349 6.3370184 5.5339694 6.3174234 6.1359941 6.5737789
## 164 6.3233723 6.5814845 5.6653035 6.4536191 6.2453811 6.8035055
## 165 3.3895736 3.2109173 4.1143880 4.8862945 4.8806677 4.3598084
## 166 3.6954711 3.6157197 4.2131394 5.0059422 4.9932905 4.5956958
## 167 4.6900326 4.9953147 3.9082140 4.9659246 4.7128309 5.3067466
## 168 3.7821411 3.6817096 4.3739904 5.0730633 5.0898201 4.6247617
## 169 3.4914483 3.3808713 4.0320910 4.8924322 4.8518244 4.4895753
## 170 3.3685457 3.2380085 3.9440732 4.8094438 4.7712289 4.4033175
## 171 3.7768534 3.4992525 4.5852079 5.3004572 5.3022864 4.7258893
## 172 3.5363112 3.3011397 4.3393208 5.0943340 5.0982617 4.5303984
## 173 2.5248736 2.0790903 3.4863302 3.8149909 3.7984380 2.9862575
## 174 1.6085836 1.4643271 2.4243650 2.9148473 2.9071359 2.3460043
## 175 1.7969874 1.6716072 2.8262061 3.0915936 3.1917095 2.3707045
## 176 1.7749345 2.3008650 1.9465474 2.0780615 2.2896660 2.0639247
## 177 1.7066694 1.7151264 2.5649321 2.6567361 2.8217387 2.0532685
## 178 1.2978846 1.3372028 2.1195509 2.4906109 2.5763602 1.9189842
## 179 1.5367932 1.7685775 1.6342305 2.2854410 2.2135839 2.1110463
## 180 2.3132847 2.4448335 1.3406629 1.7571413 1.6495258 2.0241626
## 181 3.0522984 3.0565280 1.8841321 2.5745160 2.2027482 2.9492128
## 182 2.3628993 2.2071251 2.1548619 2.3914313 2.3300707 2.0438719
## 183 2.6200332 2.5607151 1.7580535 2.4280751 2.1638891 2.5108585
## 184 2.2183365 1.9031859 1.9970943 2.5046472 2.3708140 2.1290434
## 185 2.6740114 1.9229193 3.2122673 3.4283070 3.3810844 2.5646408
## 186 2.1813847 1.6049935 2.3222762 2.5205040 2.4522083 1.8849835
## 187 3.7531166 4.0105970 2.2289672 2.6277375 2.3101266 3.3917099
## 188 2.0883658 3.2055943 2.8049856 3.0219370 3.0731065 3.0862970
## 189 2.1973350 3.3060535 2.9880167 3.0033183 3.1737964 3.0375377
## 190 2.4067450 3.4787481 2.6821211 2.8855877 2.8929476 3.1868829
## 191 2.9552832 3.8611245 3.0357083 2.9350625 3.0109656 3.2755354
## 192 2.4596499 3.3865397 2.9652674 2.8579555 3.0020406 2.9677315
## 193 2.9241983 3.8769764 2.9330321 2.8705020 2.9485731 3.2945121
## 194 3.2069244 4.0551846 3.5393115 3.3015876 3.4752828 3.5210435
## 195 2.9676933 3.8118072 3.4772888 3.2524531 3.4478393 3.3419268
## 196 4.6825805 5.7297365 4.5068371 4.5843915 4.4741076 5.1528497
## 197 3.9556646 5.1166692 4.5797452 4.5898260 4.6236345 4.8193294
## 198 3.8616334 4.9332698 4.6471353 4.6656534 4.6832306 4.7634285
## 199 3.9557599 5.0682413 4.5619696 4.6050980 4.5951743 4.8080607
## 7 8 9 10 11 12
## 2
## 3
## 4
## 5
## 6
## 7
## 8 1.5095700
## 9 2.8745287 2.0581191
## 10 1.1561304 1.0821813 1.9716672
## 11 1.8379764 1.3751490 1.7254583 0.8879389
## 12 0.7991461 1.3281029 2.4873440 0.5845270 1.2785903
## 13 1.1071829 2.2169980 3.0344240 1.7969167 2.3441110 1.6767558
## 14 2.8486373 3.5054113 4.4011938 3.2571412 3.6149378 3.0177002
## 15 2.9278040 3.2710047 4.0566979 3.0771850 3.2795024 2.9046098
## 16 2.8912887 3.6101758 4.4397342 3.3342128 3.7103776 3.0946661
## 17 3.1953155 4.1262775 5.0765999 3.8632833 4.3074314 3.5937555
## 18 2.9368276 3.1575921 3.6757917 2.9816085 3.1176053 2.9070925
## 19 3.3802027 4.1357527 4.6521104 3.8311657 4.2421904 3.6910328
## 20 2.9439039 3.4633501 4.0897504 3.2292869 3.5166705 3.0507081
## 21 3.5177223 3.4011731 3.2196693 3.2382495 3.2204558 3.3292244
## 22 2.9766296 3.1173134 3.7470312 3.0394253 3.1960924 2.9454896
## 23 3.2224328 3.1769403 3.4089372 3.0592456 2.9927608 3.0871810
## 24 3.3764594 3.2324404 3.2396777 3.1019641 3.0562698 3.1721548
## 25 3.1142168 3.1456454 3.4661806 2.9714035 3.0184994 2.9555518
## 26 3.2996035 3.4716399 3.5776610 3.1619587 3.3011580 3.1796282
## 27 3.0140633 3.1441211 3.5524505 2.9318962 3.0773530 2.8880483
## 28 3.2553846 3.3087765 3.5431539 3.0858286 3.1075201 3.1236487
## 29 3.0779270 3.1487403 3.9299983 3.0781426 3.1017524 2.9783742
## 30 3.0664505 3.2022829 4.1519715 3.1993170 3.2550891 3.0715541
## 31 3.5285890 3.3839943 3.1053030 3.1860077 3.1120833 3.3262455
## 32 3.2013217 3.3049138 3.7920368 3.1073158 3.1487193 3.0199875
## 33 4.1544224 3.9614117 3.4910275 3.8089097 3.6695942 4.0453009
## 34 3.3790833 3.3939156 3.4051534 3.1771565 3.1899284 3.2103309
## 35 3.7821396 3.6717705 3.6596206 3.5143116 3.4234829 3.6240624
## 36 2.3035559 3.0043172 3.8878187 2.7774948 3.0965457 2.5002532
## 37 2.2776451 2.9851109 3.7895780 2.7679799 3.1180170 2.5414517
## 38 2.3688392 3.3620203 4.2837226 3.0685050 3.5154064 2.7766761
## 39 2.5183681 3.4771445 4.4555458 3.2915669 3.7414771 3.0396196
## 40 3.9827942 4.7413561 5.9667253 4.6591368 5.0590897 4.4061158
## 41 4.4484656 5.1754133 6.5515228 5.1726460 5.5504561 4.9047917
## 42 3.1865370 4.2769761 5.5377467 4.0326195 4.4585891 3.7386640
## 43 2.8467378 4.0287158 5.1487889 3.7023233 4.2319541 3.4078866
## 44 2.7804147 3.9324373 5.0024344 3.6067364 4.1066365 3.3363433
## 45 1.9147166 2.9648263 3.9909599 2.5649952 3.0572151 2.2994956
## 46 2.1060808 3.2239136 4.0054996 2.7644508 3.2840020 2.5080142
## 47 2.0658597 3.0145784 3.6715908 2.6166101 3.0642187 2.4658791
## 48 2.0689894 2.0162617 2.3697544 1.6936010 1.7555771 1.8161277
## 49 3.4439873 2.8887706 1.6692419 2.7327211 2.5808153 3.1318461
## 50 1.8474807 2.3581540 2.8622063 1.9225700 2.3860358 1.9031400
## 51 1.5972150 2.4992468 3.3197716 1.9573318 2.4697434 1.8264455
## 52 1.4615982 2.3292312 3.5012981 1.8404158 2.3797786 1.5555646
## 53 2.4546912 3.5810258 4.8813443 3.2438096 3.7476134 2.9324259
## 54 2.1792785 3.3446040 4.3965952 2.9131681 3.4951825 2.6550317
## 55 4.2790627 4.6418918 5.0339762 4.3520753 4.5918508 4.3294175
## 56 5.0702280 5.5432756 6.7847294 5.5118953 5.8310897 5.3563796
## 57 4.2579745 4.8381501 5.7934495 4.5485780 4.9260934 4.3982021
## 58 4.7164791 5.1799547 6.3584793 5.0954362 5.4378019 4.9233982
## 59 2.9744816 3.8546262 4.8796570 3.4653799 3.9582025 3.2514533
## 60 2.5557573 3.3529654 4.2051163 2.9071026 3.3615417 2.7108616
## 61 2.5059801 2.9493550 3.5546566 2.5144186 2.9128688 2.4516523
## 62 2.6895538 2.7361035 3.2262332 2.3705750 2.5348814 2.3827958
## 63 2.6375228 3.1838066 4.3841583 2.9077245 3.2660071 2.6780624
## 64 2.9406599 3.5079161 4.6672348 3.2783400 3.6047300 3.1332963
## 65 3.4251932 3.6523343 5.0938224 3.6739995 3.9944690 3.5603029
## 66 3.8464752 4.7252604 5.7248599 4.4170364 4.8327843 4.1762872
## 67 3.5185386 4.2647010 4.9007864 3.8759221 4.2704290 3.7284751
## 68 2.6867837 3.7437454 4.6585422 3.3205600 3.8493324 3.0807671
## 69 2.4632881 3.3231502 3.8333544 2.7871087 3.2528425 2.6652068
## 70 2.4477594 3.4419648 4.3438249 3.0008116 3.5137484 2.7676043
## 71 3.2226377 4.2774898 5.3372500 3.9910713 4.4143759 3.7275183
## 72 2.8403728 3.8575426 4.6886854 3.4979052 3.9515847 3.2839351
## 73 3.1846121 4.3180025 5.3127497 3.9645721 4.4498225 3.6745048
## 74 3.1718163 4.2400981 5.2183482 3.9214164 4.3625045 3.6719300
## 75 3.1711167 4.2753217 5.3100505 4.0136286 4.4441263 3.7261576
## 76 2.3517797 3.2402380 4.2928208 2.9819180 3.3462868 2.7122645
## 77 2.2696537 2.7111239 3.6530573 2.5645160 2.7755947 2.3809931
## 78 2.3394206 3.2025972 4.1447447 2.9478022 3.3042588 2.6992267
## 79 2.1618605 2.8393600 3.7784982 2.5954247 2.9199776 2.4197030
## 80 2.4449904 3.4499088 4.3242374 3.1030397 3.5489456 2.8338636
## 81 2.8376425 3.7061200 5.0913724 3.5905177 3.9929483 3.2903789
## 82 2.3738609 2.9222585 4.2754750 2.8159804 3.1196971 2.5375474
## 83 2.5831389 3.5593406 4.7466158 3.3162046 3.7730449 3.0241611
## 84 2.3135756 3.2154591 4.3515956 2.9374731 3.3902357 2.6502059
## 85 2.1209268 2.9489121 4.1446213 2.7800808 3.1572508 2.5156112
## 86 2.3478096 3.0916670 4.5255646 3.0539198 3.4137114 2.7337001
## 87 2.0851720 2.8898798 3.7868177 2.6727736 3.0687528 2.4818640
## 88 2.1619054 3.0086352 4.1218187 2.8281875 3.2160380 2.5153849
## 89 2.6260207 3.0324499 4.5168914 3.1046266 3.2396774 2.7700224
## 90 2.6584777 3.2388983 4.8244404 3.3749126 3.6158435 3.0460007
## 91 2.0945825 2.8035637 4.0410548 2.7454194 3.0260569 2.4259167
## 92 2.1299212 2.7669859 4.0167406 2.7137167 2.9765083 2.3824961
## 93 2.3557721 3.1585846 4.3528831 3.0324965 3.3489699 2.7273785
## 94 2.6998340 3.7429971 4.9063076 3.5622845 4.0037780 3.2332512
## 95 2.2440438 2.7238620 3.7600399 2.6241977 2.8557832 2.3799897
## 96 2.4732586 3.1632084 4.6121769 3.2189607 3.5712550 2.9099946
## 97 2.0456506 2.6349401 3.6642317 2.5279938 2.8146020 2.2841931
## 98 4.1272933 4.2708675 6.0167538 4.6843898 4.7941448 4.4381021
## 99 4.3028188 4.7387943 6.4650530 5.0904194 5.3588343 4.8256219
## 100 3.1792615 3.5730086 5.2166656 3.8432337 4.0393718 3.5681975
## 101 3.2941250 3.5358787 4.7445986 3.7205390 3.8773957 3.5102712
## 102 3.3001367 3.7005401 4.9388736 3.8071107 3.9914793 3.5574500
## 103 4.7899018 5.0070434 5.5481919 4.8918997 4.9957297 4.8396341
## 104 3.1616199 3.3521502 4.0158272 3.3345592 3.4282104 3.2034156
## 105 3.2364642 3.4304749 4.1690827 3.4473826 3.5506359 3.2916898
## 106 3.4294433 3.4327514 3.8418244 3.4883022 3.5482898 3.4267965
## 107 3.4229848 3.3927272 3.6841066 3.4512552 3.4898685 3.4339504
## 108 3.2684664 3.4525529 4.1023523 3.4870431 3.5797501 3.3618565
## 109 3.3681995 3.4573525 4.2573616 3.5215238 3.5337293 3.3743365
## 110 3.2659355 3.3210765 3.9011162 3.3619238 3.3814114 3.2816183
## 111 3.0731275 3.6016387 4.3698169 3.5289369 3.7398396 3.3602791
## 112 2.3781569 2.7344413 3.9950182 2.8340914 2.9433203 2.5724135
## 113 2.4670540 2.5389428 3.0850356 2.5591622 2.6370353 2.4684653
## 114 2.4771324 2.4365730 2.9952918 2.4951775 2.4901586 2.4382077
## 115 2.3828255 2.8339617 3.7796914 2.7629863 2.9042947 2.4978669
## 116 2.4367370 2.6081219 3.1444682 2.5509458 2.6615420 2.4674584
## 117 2.0827518 2.6155674 3.6093979 2.5719746 2.8049916 2.3321687
## 118 2.1803379 2.6943227 3.6391072 2.5803193 2.8240815 2.3022115
## 119 2.2944175 2.6801791 3.3120389 2.6110940 2.8380226 2.4989436
## 120 2.1235990 2.7595923 3.4281602 2.5774810 2.8892548 2.3803677
## 121 3.7073122 4.0056589 4.5631225 4.0009817 4.1837520 3.8857431
## 122 3.7769015 3.9517570 4.4873821 3.9613905 4.0677311 3.8591711
## 123 3.9293948 3.8985834 4.2483609 3.9797631 4.0119140 3.9543868
## 124 4.3656315 4.1175361 3.9443547 4.1989167 4.0837137 4.3106770
## 125 3.9816960 3.9654459 4.2539353 4.0064833 4.0311001 3.9755735
## 126 3.8425851 3.9484578 4.4839956 4.0123287 4.1092689 3.9194222
## 127 4.5687890 4.3287731 3.9526769 4.3679782 4.2574198 4.5054311
## 128 4.3525144 4.3950006 4.5645233 4.3681099 4.3959576 4.3259139
## 129 4.3301582 4.3272220 4.8016704 4.3900479 4.3290161 4.3167013
## 130 4.3820294 4.4222592 4.4723801 4.3507542 4.3557567 4.3297798
## 131 4.2445498 4.3044999 4.9371715 4.3603405 4.3532946 4.2438288
## 132 4.1794922 4.2634224 4.8973677 4.3069628 4.3368219 4.1847049
## 133 4.1673165 4.2411927 5.0198023 4.3499120 4.4262907 4.2129064
## 134 4.1369026 4.2045851 4.5718284 4.1907583 4.2650993 4.1212609
## 135 4.5193554 4.5326747 4.6504140 4.4530871 4.4828958 4.4617548
## 136 4.2772476 4.2308985 4.6222137 4.2919798 4.2291202 4.2509582
## 137 4.2524448 4.2906595 4.5691846 4.2898654 4.3024987 4.2464070
## 138 4.3277146 4.3603976 4.8478918 4.3942655 4.3337387 4.3081755
## 139 4.5637190 4.4888364 4.4204399 4.4594321 4.3603833 4.4870728
## 140 4.3790799 4.3168437 4.5849267 4.3839004 4.3232628 4.3608015
## 141 4.6468080 4.4994577 4.3981900 4.5221764 4.3457551 4.5916347
## 142 5.5729025 5.2216898 4.4234339 5.2746461 5.1501321 5.4789006
## 143 6.2849604 6.1301278 5.8037140 6.1338791 6.0527372 6.2173981
## 144 4.8056177 4.5825177 4.2379605 4.6322197 4.5425375 4.7374671
## 145 5.2320412 5.0442409 4.3622263 4.9975132 4.9315242 5.1356044
## 146 5.4273349 5.1786682 4.8627631 5.1904238 5.0085585 5.3541549
## 147 5.0096916 5.0526506 5.1388477 4.9724307 5.0275193 4.9811148
## 148 5.1369601 4.9234795 4.2985824 4.9243804 4.8837804 5.0694716
## 149 4.8995136 4.6722989 4.2284875 4.7313480 4.7058442 4.8713906
## 150 4.4872316 4.4342661 4.3465280 4.4155018 4.3930654 4.4521903
## 151 4.1728044 4.2108180 4.7720070 4.3128932 4.3669189 4.2180955
## 152 4.3299208 4.4441749 4.7944717 4.4383258 4.6009517 4.3443692
## 153 5.9304996 6.1685041 6.3215586 6.0410885 6.2102915 5.9506990
## 154 4.4780103 4.5106177 4.7910878 4.5189999 4.6073467 4.4896055
## 155 5.8016330 5.8516115 6.1332300 5.8418979 5.8439550 5.7974310
## 156 6.6286420 6.7631139 6.9577843 6.6668748 6.7026812 6.6621935
## 157 5.5371856 5.6691223 5.6278748 5.4910161 5.5982242 5.5096901
## 158 3.9246244 3.9597815 5.6093553 4.4819557 4.7362232 4.2308222
## 159 3.1105945 3.3992699 4.5096597 3.5066170 3.7551095 3.2289090
## 160 4.2800300 4.4442654 5.3735591 4.5498626 4.6478761 4.3522414
## 161 5.0245709 5.2470772 6.1498479 5.3486562 5.5396882 5.1557186
## 162 4.8074552 4.8369295 6.6221844 5.4279026 5.6827420 5.1741941
## 163 6.4015692 6.3594650 7.8400047 6.8516075 7.0076476 6.6564128
## 164 6.6888874 6.6153765 8.0921498 7.1147072 7.1998974 6.9405241
## 165 2.6813645 2.9105945 3.7850223 2.9789192 3.2179770 2.7817790
## 166 3.2485003 3.4511916 4.3898064 3.5315280 3.7691662 3.3796786
## 167 5.0681457 4.9750809 6.7282320 5.6017793 5.7608840 5.3892176
## 168 3.1513077 3.4564592 4.1986271 3.4472954 3.7239775 3.3372132
## 169 3.0504736 3.1758229 4.1471636 3.3073811 3.4495871 3.1514792
## 170 2.9075147 3.0494596 4.0255957 3.1536873 3.2565146 2.9849239
## 171 3.0029512 3.1466522 3.6076367 3.0553403 3.1647176 2.9815923
## 172 2.8364694 3.0292133 3.7219248 2.9943144 3.1575196 2.8353916
## 173 2.0293374 2.2264354 3.0058073 2.3153262 2.6446758 2.1645481
## 174 1.9752471 2.4396862 3.7987896 2.5380520 2.7729403 2.2087917
## 175 1.7573578 2.5648857 3.6708289 2.4749562 2.8947195 2.1358747
## 176 2.4191602 3.4545390 4.9174949 3.4457838 3.8843581 3.0749859
## 177 1.5898393 2.6797369 3.8135171 2.4881865 2.9573033 2.1616489
## 178 1.7861830 2.5710988 4.0431447 2.5563202 2.9477940 2.1424503
## 179 2.3078958 2.7746116 4.4378780 3.0337125 3.2986082 2.7007802
## 180 3.1851524 3.6626310 5.3362091 3.9865391 4.3163150 3.6809384
## 181 3.8989966 3.8990313 5.5969838 4.4254177 4.5286865 4.2167644
## 182 2.7010503 3.1308062 4.5706756 3.4692896 3.9063491 3.2191385
## 183 3.4792107 3.5715854 5.3043828 4.0461759 4.2675047 3.7727164
## 184 2.8828933 3.0620123 4.6590057 3.4150319 3.7049120 3.1158557
## 185 2.3863086 2.4916156 3.3812592 2.6687219 3.0214228 2.5353653
## 186 2.1817455 2.5164266 3.7540944 2.7457380 3.0989561 2.5705711
## 187 4.5930607 4.7950241 6.5871058 5.3143400 5.5768155 5.0821518
## 188 2.7470780 3.4855271 4.9884247 3.5895530 3.9628790 3.2903887
## 189 2.7537151 3.7241299 5.1477072 3.6459824 4.1092283 3.3144377
## 190 3.1371539 3.7763677 5.3976718 3.9313309 4.2698178 3.6468310
## 191 3.3429318 4.0717382 5.6213318 4.1169658 4.5736432 3.8710668
## 192 2.8159373 3.6780594 5.1542383 3.5678908 4.0323156 3.2786094
## 193 3.4832746 4.2042632 5.8284165 4.2497020 4.6694522 3.9700336
## 194 3.6599803 4.5173314 5.8150625 4.3976567 4.8163145 4.1471065
## 195 3.4018398 4.2921814 5.5719637 4.1195723 4.5672839 3.8528510
## 196 5.4367967 5.7439911 7.3610170 6.0739917 6.3723548 5.8730198
## 197 4.4541724 4.9570130 6.3013360 4.9500608 5.2492765 4.7501410
## 198 4.1557499 4.5880705 5.7440432 4.5389191 4.8020970 4.4124494
## 199 4.3687651 4.7662419 6.0846069 4.8158329 5.0958174 4.6559723
## 13 14 15 16 17 18
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14 3.0658834
## 15 3.3405234 0.9367744
## 16 3.0273470 0.2758607 1.1202682
## 17 3.0812139 1.2244857 2.1108514 1.0757216
## 18 3.2210395 1.2110406 0.6594929 1.3021093 2.2670798
## 19 3.1757532 1.7634207 2.2152181 1.5714186 1.5506513 2.1446790
## 20 3.1422967 0.7760617 0.8333488 0.7344435 1.7201299 0.7805656
## 21 3.7543230 2.4361579 1.8494246 2.4581713 3.3946342 1.3154506
## 22 3.3590267 1.2945799 0.6330267 1.4155829 2.4007106 0.3948462
## 23 3.5098177 1.9478842 1.2929166 2.0356418 2.9500481 0.7681670
## 24 3.6855687 2.2417421 1.5809335 2.3076665 3.2749855 1.0670601
## 25 3.4687378 1.6971508 0.9985836 1.7955823 2.7977743 0.5559626
## 26 3.5057440 1.9663902 1.4803126 1.9753820 2.8308425 1.1795657
## 27 3.3631827 1.4570015 0.8081145 1.5522362 2.5642662 0.4681726
## 28 3.5170471 1.9760560 1.3353867 2.0483006 2.8862558 1.0363280
## 29 3.5549193 1.5559369 0.7622008 1.7606632 2.6467553 0.8984443
## 30 3.5100756 1.4985741 0.9221360 1.7111243 2.4487243 1.1312965
## 31 3.7063159 2.5256616 1.9543666 2.5518855 3.4368612 1.3933969
## 32 3.6636673 1.6887085 0.8028575 1.8250284 2.8418720 0.7827940
## 33 4.1241813 3.4509351 2.9971942 3.4485379 4.0415490 2.5354553
## 34 3.6462415 2.1239708 1.4854382 2.1559574 3.1090615 1.0161662
## 35 4.0161425 2.8085107 2.1570952 2.8611079 3.6128024 1.8704692
## 36 2.5956534 1.2158608 1.2884726 1.2149789 1.8896180 1.3767497
## 37 2.4259026 1.2704413 1.4440919 1.2134752 1.7724882 1.4088364
## 38 2.3121493 1.2784969 1.9078408 1.1501970 1.1797285 1.9737485
## 39 2.2954021 1.6326126 2.3046013 1.5099638 1.1567134 2.3152134
## 40 3.9392379 4.2486582 4.6645126 4.2559818 3.9308291 4.8232053
## 41 4.4336113 4.6769290 5.1054210 4.7035406 4.2883681 5.3089880
## 42 2.8977089 3.0935551 3.7403357 3.0715021 2.3951258 3.9145116
## 43 2.4780495 2.7374517 3.4507410 2.6651818 2.0177826 3.5809097
## 44 2.3597336 2.7124404 3.4114324 2.6396977 2.0252307 3.5015236
## 45 1.8411603 1.9500547 2.4249249 1.9326322 1.9072676 2.5028584
## 46 1.8369088 2.0376685 2.5741840 1.9331701 1.8921835 2.5662104
## 47 1.6542187 2.1657056 2.6189083 2.0719375 2.0731978 2.4877462
## 48 2.4159628 2.4869198 2.1734135 2.5642044 3.2645166 1.9307652
## 49 3.4917212 3.9528167 3.5997698 3.9680759 4.6715888 3.1075571
## 50 1.8861665 2.1944608 2.3165836 2.1875955 2.6520748 2.1323246
## 51 1.4616671 2.7291765 3.0041162 2.7317997 2.8663567 2.9656312
## 52 1.8816201 2.5832088 2.7419013 2.6517204 2.9238854 2.8613113
## 53 2.3180172 3.1211934 3.6501090 3.1325306 2.7657673 3.8280270
## 54 1.8470525 2.9595513 3.5069078 2.9240370 2.6404197 3.5832149
## 55 4.2214922 3.9416093 4.1185283 3.9456938 4.0800968 4.0634488
## 56 5.0917371 5.6107683 5.9463628 5.6753855 5.3829708 6.1188737
## 57 4.2985044 4.9753868 5.2710954 5.0176747 4.9120190 5.4122009
## 58 4.8502044 5.9166021 6.1557419 5.9756798 5.8435154 6.3227036
## 59 2.8926584 2.4923936 3.0692903 2.5059904 2.2481262 3.2328579
## 60 2.5985724 1.9710988 2.3962575 1.9869505 2.1250002 2.4991957
## 61 2.6856640 2.1256306 2.2510899 2.1754675 2.6525442 2.2272907
## 62 3.1448464 2.3997598 2.0639207 2.5210690 3.2708264 2.0406405
## 63 3.0470505 2.1339504 2.2974489 2.2841693 2.5693507 2.5798532
## 64 3.0309986 2.6337283 2.9805330 2.7381415 2.6592574 3.1398616
## 65 3.7464012 3.6559394 3.8528945 3.8110798 3.7878109 4.0721357
## 66 3.7187246 4.7677200 5.1556388 4.7563732 4.5157672 5.2777769
## 67 3.3551001 4.5844450 4.8737987 4.5561278 4.5132369 4.8862000
## 68 2.4098931 2.3318883 2.9939615 2.2647202 1.9182814 3.0755725
## 69 2.1946056 2.2234242 2.6699355 2.1478615 2.2485881 2.5826643
## 70 2.2962518 2.0974585 2.6735845 2.0568324 1.9261270 2.7548945
## 71 2.8942229 2.5716798 3.2717963 2.5054706 1.8155474 3.3927253
## 72 2.4708739 2.1637126 2.8309645 2.0545569 1.6072512 2.8503097
## 73 2.8573613 2.4522021 3.2086861 2.3504758 1.6739270 3.3364188
## 74 2.7931610 2.5153754 3.2266158 2.4263665 1.7479338 3.3159307
## 75 2.8081119 2.6568665 3.3452747 2.5596543 1.9036959 3.4358900
## 76 2.3932076 1.8175092 2.2053372 1.8150430 1.8380632 2.3200960
## 77 2.6336406 1.8766502 1.7311068 1.9538055 2.4979941 1.7743444
## 78 2.3342066 1.8000659 2.1622774 1.7658503 1.8625020 2.2031467
## 79 2.2439954 1.8106215 2.0407377 1.8383201 2.0873888 2.0427850
## 80 2.3125679 1.8710507 2.4020540 1.7824609 1.7249212 2.4467013
## 81 2.8957432 2.5287892 3.0225366 2.5757213 2.2378359 3.2503046
## 82 2.8493868 2.1144538 2.1890889 2.2558917 2.5476990 2.4567543
## 83 2.5354733 2.2216492 2.7795044 2.2159162 1.9278673 2.9431994
## 84 2.4265884 1.9431499 2.3725896 1.9622897 1.9740498 2.5401758
## 85 2.2291489 1.7792363 2.1576309 1.8163360 1.8540564 2.2732080
## 86 2.6681363 1.9655322 2.2520461 2.0593963 2.0961795 2.5099097
## 87 1.9887876 1.7879013 2.1692171 1.7436291 1.8646139 2.1028550
## 88 2.3821266 1.6398723 1.9279501 1.6453882 1.8965272 2.0639662
## 89 3.2859195 2.5715026 2.3868271 2.7292435 3.1114459 2.7069901
## 90 3.0831831 2.6178532 2.7330010 2.7331647 2.7762316 3.0029364
## 91 2.4720602 2.0163575 2.0716007 2.0700625 2.3839567 2.2168799
## 92 2.6193311 2.0422541 1.9947500 2.1183369 2.5355509 2.1783941
## 93 2.5571579 2.3415207 2.5595854 2.3686332 2.4647957 2.6949052
## 94 2.5989812 2.5824300 3.0916111 2.5297997 2.2277568 3.2195150
## 95 2.6836479 2.3340841 2.2283329 2.3982008 2.8775667 2.3010924
## 96 2.7904695 2.3466029 2.5419074 2.4136488 2.4283842 2.7706635
## 97 2.3844751 1.9854649 1.9750839 2.0230801 2.4722417 2.0048852
## 98 4.6201177 4.1485917 4.1409676 4.3127739 4.2955539 4.4318481
## 99 4.4944527 4.2838829 4.5802746 4.3779339 3.9994443 4.8259726
## 100 3.5695951 3.1548716 3.2574559 3.2827209 3.2452848 3.5065037
## 101 3.7066260 1.8322984 1.6704656 1.9823950 2.4139829 1.8937334
## 102 3.6617117 1.7296252 1.7270187 1.8666827 2.1719706 2.0082124
## 103 5.0245312 3.8962907 3.5515866 3.9314864 4.2360095 3.6702309
## 104 3.5155180 1.6092910 1.0929518 1.6887161 2.5342841 0.9763982
## 105 3.6307863 1.6918023 1.1785728 1.7785593 2.5989637 1.1663883
## 106 3.7702553 2.1609120 1.6172328 2.2006036 3.0624350 1.3196472
## 107 3.6815892 2.2272065 1.7425882 2.2482514 3.0712172 1.3229909
## 108 3.5773845 1.7872809 1.3580437 1.8362953 2.5975904 1.2024136
## 109 3.8344751 1.9680058 1.3457322 2.1002355 2.8961901 1.4024529
## 110 3.6137215 1.9015314 1.3250659 1.9845140 2.8060287 1.0986841
## 111 3.1086516 1.3225284 1.5402846 1.2783647 1.6433518 1.4305905
## 112 2.9023120 2.3714000 2.1578115 2.4783874 2.9281760 2.2896774
## 113 2.8867177 2.5718980 2.1808952 2.6044565 3.3269320 1.9841241
## 114 2.9227180 2.6365304 2.1905018 2.6920583 3.4214936 1.9833778
## 115 2.8650550 2.2786849 2.0074289 2.3315832 2.9269740 2.0706232
## 116 2.8022129 2.5232595 2.1418661 2.5440618 3.2136160 1.9752291
## 117 2.4322106 2.0715531 1.9829764 2.0993326 2.5865090 1.9696852
## 118 2.6697324 2.0960346 1.8939621 2.1365432 2.7620940 1.9510981
## 119 2.4903803 2.3589634 2.1908892 2.3386940 2.8478472 2.0241062
## 120 2.2584331 2.1017015 2.1249103 2.0481281 2.5327362 1.9805444
## 121 3.8300071 3.1925567 3.1568451 3.1737576 3.5203284 3.0554323
## 122 4.0258328 3.2841141 3.0854511 3.3003505 3.7740064 3.0085644
## 123 4.1837800 3.5529777 3.2545991 3.5763371 4.1254780 3.0865750
## 124 4.5040332 4.1528365 3.7738486 4.1597196 4.7577980 3.4369867
## 125 4.2512735 3.5864178 3.2633034 3.6062597 4.1919539 3.0970693
## 126 4.1181321 3.3770285 3.1504321 3.3988113 3.8956975 3.0615471
## 127 4.6450653 4.3724237 4.0056379 4.3575454 4.9555178 3.6269837
## 128 4.5897963 3.2371512 2.8788778 3.2394036 3.9171025 2.6712046
## 129 4.6609663 3.2134381 2.7914020 3.2805370 3.9040800 2.7039566
## 130 4.5846435 3.2932949 2.9349392 3.2870243 3.9774434 2.6842343
## 131 4.6278251 3.0549893 2.6616761 3.1381593 3.7446084 2.6739104
## 132 4.5589601 2.9580960 2.5924843 3.0348622 3.6461863 2.6065627
## 133 4.5773036 2.9515083 2.6212077 3.0408886 3.6011044 2.6914869
## 134 4.4303588 2.9518553 2.6125275 2.9811221 3.6480801 2.4903450
## 135 4.7520749 3.4976196 3.0599952 3.5092221 4.1324324 2.9124046
## 136 4.5817460 3.1958874 2.7707380 3.2576620 3.8976666 2.6289181
## 137 4.4964722 3.1220078 2.7567147 3.1421705 3.7825225 2.5777351
## 138 4.6650627 3.1838423 2.7605169 3.2521615 3.8758417 2.6978345
## 139 4.7502416 3.5901167 3.1600091 3.5957980 4.2882601 2.8540930
## 140 4.6411970 3.3319088 2.9186442 3.3695221 4.0157872 2.7134748
## 141 4.7764483 3.7635189 3.3356993 3.7774834 4.4081754 2.9853137
## 142 5.5537410 5.0022528 4.6410790 4.9580434 5.6026314 4.1318812
## 143 6.3577362 6.9143938 6.6803554 6.8983408 7.3301298 6.4500820
## 144 4.9157558 5.6130769 5.3330915 5.5993778 6.1045127 5.0553945
## 145 5.2469097 5.9878839 5.7291118 5.9442101 6.4684827 5.3962534
## 146 5.5094864 6.1850401 5.8041144 6.1894005 6.6133777 5.5846123
## 147 5.2183474 5.6650182 5.3655152 5.6598301 6.0580037 5.2959747
## 148 5.1436650 5.9250224 5.6832304 5.8828331 6.3844754 5.3494283
## 149 4.9273448 5.7267113 5.4836876 5.6952951 6.1602688 5.1779458
## 150 4.6367337 5.2699373 5.0132572 5.2579359 5.7203715 4.8179008
## 151 4.5115523 4.9412165 4.7238880 4.9712864 5.3656830 4.6891453
## 152 4.6403067 5.0355236 4.8337471 5.0327311 5.4684160 4.7862086
## 153 6.0789789 6.4110704 6.3172555 6.3789895 6.6970432 6.2711381
## 154 4.7391689 5.2102456 4.9530824 5.2149874 5.6186780 4.8874945
## 155 6.0164730 6.3733340 6.1708985 6.3904761 6.7180988 6.1312760
## 156 6.7263154 7.1192614 6.9201792 7.1166430 7.3209000 6.9049463
## 157 5.6662142 6.1128193 5.8503238 6.0854157 6.4350630 5.7866856
## 158 4.5328954 4.7849277 4.6975674 4.8899257 5.0439472 4.9098506
## 159 3.7185625 4.0283269 3.8329816 4.0791036 4.4841571 3.9720626
## 160 4.7490116 4.9523399 4.7582984 5.0128320 5.3463250 4.8701801
## 161 5.3994770 5.6377511 5.5425913 5.6763973 5.8993894 5.6627149
## 162 5.3573489 5.5443186 5.5403822 5.6621566 5.6624760 5.7923840
## 163 6.8730398 6.9875066 6.9444542 7.0993180 7.1292125 7.1565086
## 164 7.1281342 7.2774397 7.2225655 7.3989968 7.3990399 7.4258627
## 165 3.1673780 3.8177344 3.6584175 3.8460136 4.2857664 3.6584150
## 166 3.7021742 4.2234362 4.0063118 4.2622673 4.5913615 4.0932181
## 167 5.6227251 5.8168986 5.7492709 5.9517555 5.9788493 5.9840959
## 168 3.4160135 4.1684950 4.0290931 4.1704927 4.4385747 4.0445930
## 169 3.5558437 4.0919547 3.8336111 4.1463229 4.5324072 3.8944415
## 170 3.4275958 3.9874805 3.7297144 4.0472740 4.4534053 3.7826480
## 171 3.3809823 4.0784935 3.7894250 4.0964814 4.5764777 3.7401539
## 172 3.3275785 3.9186721 3.6636652 3.9490597 4.4429285 3.6630514
## 173 2.4940858 2.7667806 2.5747993 2.7735715 3.3736228 2.4465667
## 174 2.6190991 2.5935565 2.4330265 2.6749311 3.1204834 2.5689731
## 175 2.1425206 2.3760722 2.4394221 2.3657335 2.7321993 2.4841968
## 176 2.4459258 2.8315030 3.2685474 2.8227563 2.5044690 3.4421818
## 177 1.6158067 2.3035498 2.6146234 2.2645753 2.3332697 2.6421739
## 178 2.4017128 2.3933430 2.4365751 2.4625918 2.7702644 2.6555309
## 179 2.8791581 2.8771492 2.8756059 2.9832514 3.1609945 3.0941650
## 180 3.5362562 3.1678402 3.3781750 3.2548824 3.1399079 3.6172162
## 181 4.4081212 4.0157807 3.9410086 4.1696113 4.2456926 4.1614943
## 182 2.9827208 2.7552503 2.9706666 2.7824232 2.8305537 3.0601122
## 183 4.1164454 3.5221408 3.4306908 3.6736034 3.8643990 3.7145712
## 184 3.5832870 2.8945670 2.7530988 3.0301491 3.4020220 3.0246623
## 185 2.8461126 2.5495164 2.3723142 2.5787439 3.1781484 2.2869461
## 186 2.4867112 2.3703368 2.4229662 2.4112638 2.6994298 2.4062620
## 187 4.8987688 4.6849962 4.8816071 4.7989849 4.5382911 5.1174864
## 188 2.8788345 4.0268711 4.2891257 4.0577780 3.8899854 4.4254809
## 189 2.7587774 3.9842811 4.3555628 3.9899782 3.7202838 4.5162851
## 190 3.3046848 4.3411976 4.6112326 4.4015169 4.1731417 4.7903091
## 191 3.3306998 4.5527559 4.9545383 4.5950760 4.2233525 5.1283081
## 192 2.8763102 4.1334915 4.4990868 4.1747764 3.9195616 4.6810846
## 193 3.5755562 4.6257515 5.0002823 4.6872053 4.3400049 5.2193314
## 194 3.5040564 4.6842237 5.1234480 4.6919803 4.2984962 5.2650198
## 195 3.3142562 4.4673927 4.8735588 4.4760094 4.1540865 5.0306354
## 196 5.5938423 6.5694578 6.8296409 6.6493488 6.3382055 7.0247946
## 197 4.5709944 6.1314324 6.3678523 6.1931731 6.0041925 6.5341885
## 198 4.2058387 5.9654118 6.1499004 6.0175405 5.8842237 6.2564621
## 199 4.4867527 6.1141018 6.3208990 6.1795070 6.0212099 6.4586176
## 19 20 21 22 23 24
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20 1.6771344
## 21 2.8186388 1.7947947
## 22 2.3253926 0.8753478 1.3778455
## 23 2.7306608 1.4757338 0.9514578 0.8795849
## 24 2.8961673 1.6804166 0.4678080 1.1052409 0.5856703
## 25 2.5877917 1.2246890 0.9386681 0.6138878 0.5142981 0.5968183
## 26 2.0326047 1.4616627 1.1563890 1.3448369 1.3639767 1.2662570
## 27 2.3120378 1.0179633 1.1134941 0.5518461 0.8421166 0.8895967
## 28 2.2886332 1.5736221 1.2452115 1.2058629 1.0520402 1.1680367
## 29 2.7817191 1.4566608 1.8611169 0.8292822 1.0648474 1.4763267
## 30 2.7022029 1.5419987 2.2163823 1.0691780 1.3913356 1.8595110
## 31 2.8209744 1.9476845 0.4419368 1.5387391 0.9622728 0.6275843
## 32 2.6872770 1.3037004 1.3437198 0.7276457 0.8906101 1.0462541
## 33 3.0169828 2.9849440 1.9986559 2.7204462 2.2504960 2.1955020
## 34 2.5451019 1.4954695 0.4773030 1.1104710 0.8032154 0.5489128
## 35 2.7612187 2.3550322 1.5960194 1.9744028 1.6690282 1.6692873
## 36 2.0528141 1.0693359 2.3037338 1.3982257 1.8974606 2.1575058
## 37 1.7355778 1.0772404 2.2689404 1.4815246 1.9370050 2.1803962
## 38 1.6953707 1.4821613 2.9682682 2.0932323 2.5801050 2.8645760
## 39 1.7682225 1.8820456 3.3037967 2.4347317 2.8838763 3.2030626
## 40 4.5542105 4.6156481 5.7074723 4.8712212 5.2433279 5.5436775
## 41 5.0371100 5.1107364 6.2798373 5.3410869 5.7355388 6.0834310
## 42 3.3441972 3.6310350 5.0238237 4.0545652 4.4356608 4.8403310
## 43 2.8200479 3.2109297 4.6039025 3.7292635 4.1510634 4.4765796
## 44 2.8211445 3.1630670 4.5027623 3.6632478 4.0406653 4.3721619
## 45 2.4124612 2.2874538 3.4336546 2.6504433 3.0099465 3.2864067
## 46 2.2008014 2.2210090 3.3553963 2.7314832 3.0773417 3.2864880
## 47 2.2429526 2.2680439 3.1847896 2.6794511 2.9041503 3.1219548
## 48 3.1345627 2.3133919 2.1391912 2.0366423 1.9146824 1.9770701
## 49 4.1453981 3.5463970 2.4247210 3.2166180 2.7787448 2.5155402
## 50 2.5963801 2.1628004 2.5764830 2.2764178 2.4387309 2.5015463
## 51 3.1135444 2.9309413 3.6107049 3.1229019 3.3067837 3.4867546
## 52 3.2903387 2.8515005 3.6115701 2.9432415 3.2377684 3.4264958
## 53 3.5603862 3.6194229 4.8346590 3.9494843 4.3197482 4.6463524
## 54 3.2025965 3.3457118 4.4432278 3.7295650 4.0702435 4.3168721
## 55 4.2202213 4.0721029 4.4996215 4.1909450 4.2957429 4.4085069
## 56 6.0663730 6.0709113 6.9891381 6.1743722 6.4694673 6.7706390
## 57 5.4101638 5.3493427 6.1264144 5.4991972 5.7633035 5.9593171
## 58 6.3648329 6.2751553 7.0467371 6.3550162 6.6390751 6.8623917
## 59 2.9932559 3.0348045 4.2254262 3.3854531 3.7783598 4.0485307
## 60 2.6088094 2.3476801 3.3817924 2.6548453 3.0079923 3.2212780
## 61 2.7959030 2.2833532 2.8359387 2.3650762 2.6010814 2.6903932
## 62 3.2314929 2.3755298 2.4096214 2.1118498 2.1867328 2.2120770
## 63 3.2107800 2.6088831 3.5796979 2.6349272 3.0308380 3.3058751
## 64 3.4158149 3.1724646 4.1556818 3.2674984 3.5535284 3.8947157
## 65 4.5263082 4.1932985 5.0260188 4.1019497 4.4231130 4.7279797
## 66 5.0005902 5.0858307 6.0255533 5.3732261 5.6630847 5.8980604
## 67 4.7291130 4.7505523 5.3995857 4.9975914 5.1919926 5.3294550
## 68 2.5662114 2.7567625 4.0054205 3.2468014 3.6329353 3.8878246
## 69 2.4141582 2.3919420 3.2353461 2.7971642 3.0248984 3.1723104
## 70 2.4936749 2.4907967 3.6650971 2.9205124 3.2953691 3.5346831
## 71 2.6966036 3.0513094 4.4597186 3.5575774 3.9378581 4.3138265
## 72 2.1235069 2.4984862 3.7736807 3.0422086 3.3917364 3.6853197
## 73 2.5269401 2.9068696 4.3644968 3.4984441 3.9257162 4.2490964
## 74 2.5163096 2.9544481 4.3361768 3.4938460 3.8663260 4.2162093
## 75 2.6920120 3.0358045 4.4443262 3.5811422 3.9663467 4.3257458
## 76 2.3441532 2.0986599 3.3126524 2.4319383 2.8084124 3.1471820
## 77 2.5939998 1.8473596 2.5505739 1.8036936 2.0787147 2.3598529
## 78 2.2218833 1.9600205 3.1145281 2.3190944 2.6688569 2.9803728
## 79 2.3978571 1.9908351 2.9259073 2.1699221 2.4490013 2.7526704
## 80 2.1542767 2.0824875 3.3337752 2.5840340 2.9732251 3.2351485
## 81 3.1593180 3.0463555 4.3726155 3.3152678 3.7559819 4.1458959
## 82 3.1427573 2.4694984 3.4666691 2.4538932 2.8613274 3.1929418
## 83 2.7172093 2.6699141 3.9871306 3.0457375 3.4783272 3.8108433
## 84 2.5687856 2.3160257 3.5313044 2.6282065 3.0647052 3.3558203
## 85 2.4783472 2.1175272 3.3108817 2.3585266 2.7500785 3.1077420
## 86 2.8293637 2.3665001 3.6201080 2.5096894 2.9912712 3.3756922
## 87 2.1519522 1.9058373 2.9476792 2.2299529 2.5471057 2.8271627
## 88 2.3176464 1.7944780 3.0253287 2.0964294 2.5625255 2.8635373
## 89 3.6406774 2.7670865 3.6476001 2.6056204 2.9735341 3.3486295
## 90 3.4836317 2.9411584 4.0613641 2.9460665 3.3644836 3.7879242
## 91 2.7453238 2.0941987 3.1189295 2.1971431 2.5868082 2.9236090
## 92 2.8685761 2.0907691 3.0520900 2.1253691 2.5286207 2.8441146
## 93 2.9336878 2.5299145 3.5987764 2.7272477 3.0862732 3.4178492
## 94 2.8402049 2.8637592 4.1672585 3.2885435 3.7167774 4.0379144
## 95 3.0633362 2.3034350 2.9750647 2.2777577 2.5604888 2.7953756
## 96 2.9090844 2.6170550 3.7761249 2.7386915 3.2135611 3.5760181
## 97 2.6341316 1.9412291 2.7562282 2.0070849 2.3342284 2.5954671
## 98 5.0590037 4.5142644 5.4387497 4.3152116 4.6686193 5.1091905
## 99 4.8757677 4.7319967 5.9199279 4.7660457 5.1935235 5.6461610
## 100 3.9850811 3.5036536 4.5477909 3.4355771 3.8184021 4.2566445
## 101 2.8641884 1.9351248 2.9317740 1.7342001 2.2240106 2.6454635
## 102 2.7718126 1.9450966 3.1388170 1.9031592 2.4101173 2.8587043
## 103 3.3338078 3.7519365 3.9719752 3.6985195 3.8721982 4.0149527
## 104 2.4741547 1.1711577 1.6959207 0.8400769 1.1810324 1.4793855
## 105 2.5701715 1.2924717 1.8741684 0.9800151 1.3804511 1.6621775
## 106 2.7485581 1.5539398 1.3893677 1.1454727 1.2565280 1.3014235
## 107 2.7018774 1.6034448 1.2617503 1.2213336 1.1743147 1.2126031
## 108 2.4627788 1.3180688 1.8010447 1.0721664 1.3593973 1.6402243
## 109 2.9595674 1.6791411 2.0841084 1.2141864 1.4602912 1.8023823
## 110 2.6712735 1.4447617 1.6028454 0.9731500 1.0733463 1.3791479
## 111 1.8355039 1.1942240 2.4035434 1.5180358 1.8701233 2.2616144
## 112 3.2268698 2.3653877 3.0862648 2.2081718 2.4859218 2.8415668
## 113 3.0883843 2.1415994 2.1076254 1.9073206 1.9657758 2.0319698
## 114 3.2252790 2.2379769 2.1108579 1.9126793 1.8871896 1.9904778
## 115 2.9692221 2.0634606 2.6654273 2.0027028 2.2640304 2.5072097
## 116 2.7979616 2.1081422 2.1430886 1.9454093 2.0292703 2.1164465
## 117 2.6696107 1.9150227 2.6477957 1.9444966 2.2371172 2.5011405
## 118 2.7972614 1.8826785 2.5517301 1.8824123 2.2223767 2.4119963
## 119 2.4207488 2.0094111 2.3658036 2.0380228 2.2187392 2.3608948
## 120 2.3758393 1.8053660 2.4564178 2.0171385 2.2718025 2.4220953
## 121 3.4099410 2.9855265 3.3835184 3.0413260 3.2162413 3.3430079
## 122 3.6176829 3.0379662 3.2593644 2.9659364 3.0915583 3.1998900
## 123 3.8566432 3.2233235 3.1219004 3.0330020 3.0416790 3.0878429
## 124 4.2738187 3.7034939 3.0784047 3.4346758 3.1838594 3.1311960
## 125 3.8951799 3.2280299 3.0770675 3.0435081 3.0403486 3.0576929
## 126 3.7393180 3.1093184 3.2676723 2.9942125 3.1162376 3.2074567
## 127 4.3523966 3.8731051 3.1282834 3.6435596 3.3590841 3.2482272
## 128 3.5650916 2.7757676 2.5550503 2.6187710 2.5993608 2.5700098
## 129 3.8201218 2.9128490 2.9110663 2.6273539 2.6042253 2.7692605
## 130 3.5941830 2.8098649 2.4776149 2.6631463 2.5715448 2.5152609
## 131 3.7575121 2.8336776 3.0362442 2.5743345 2.6744745 2.8640928
## 132 3.6538704 2.7342072 2.9724045 2.5025200 2.6436684 2.8122994
## 133 3.6501239 2.7919821 3.1535153 2.5553548 2.7951929 2.9807908
## 134 3.4140636 2.5907834 2.5907691 2.4183867 2.5130594 2.5387186
## 135 3.4061714 3.0768810 2.7550070 2.9050633 2.8859670 2.8457745
## 136 3.7555178 2.8697586 2.7581397 2.5664981 2.5005102 2.6341157
## 137 3.4748892 2.7194506 2.5980983 2.5317281 2.5184873 2.5673735
## 138 3.8039500 2.8953388 2.9349081 2.6279548 2.6142399 2.7889408
## 139 3.8687087 3.0870910 2.5309907 2.8478669 2.6042397 2.5638317
## 140 3.7786545 2.9312288 2.6964938 2.6529173 2.5513325 2.6282887
## 141 4.0097156 3.2940477 2.6902184 3.0089411 2.6567160 2.6928858
## 142 4.8796288 4.3921553 3.2588999 4.1545105 3.7552993 3.4907795
## 143 6.9515487 6.5739539 6.1283881 6.4508461 6.2859126 6.2011284
## 144 5.6788460 5.2124837 4.6832239 5.0457515 4.8591488 4.7638408
## 145 5.9079641 5.5219068 4.8541360 5.4115541 5.1886810 5.0099541
## 146 5.8597324 5.8261514 5.2589250 5.6220106 5.3930285 5.3683168
## 147 5.3504063 5.3646982 5.1593201 5.2891556 5.3053023 5.2668316
## 148 5.8277989 5.4737727 4.8373876 5.3584880 5.1579474 4.9879799
## 149 5.5998504 5.3113893 4.7584109 5.1795298 5.0146755 4.8880748
## 150 5.2917331 4.9208758 4.6009224 4.8112548 4.7154017 4.6667833
## 151 5.2392834 4.7478875 4.8182246 4.6227637 4.7010626 4.7674417
## 152 5.1392599 4.7674301 4.7697873 4.7195115 4.8471845 4.8061089
## 153 6.3874627 6.1870110 6.2373877 6.2495070 6.3570449 6.3026618
## 154 5.1307690 4.9408390 4.8447842 4.8495652 4.9097430 4.8976550
## 155 6.4916093 6.1970611 6.1741667 6.1109399 6.1214319 6.1626443
## 156 6.7350455 6.9533025 6.9353370 6.9332822 6.9543369 7.0031471
## 157 5.5557130 5.8099344 5.6072278 5.8081036 5.8413242 5.7699136
## 158 5.3679635 4.8999431 5.5639271 4.7239636 5.1340737 5.3682199
## 159 4.4649601 3.9161917 4.3534448 3.8409476 4.1585583 4.2621578
## 160 5.4092522 4.8873932 5.2291720 4.7756518 4.9728678 5.1126655
## 161 5.9293295 5.6079394 6.0261407 5.5732757 5.8303693 5.9448917
## 162 6.1707153 5.7721368 6.5698095 5.6044290 6.0451412 6.3360673
## 163 7.5930108 7.1810804 7.8135856 6.9969564 7.3324835 7.5913214
## 164 7.9052874 7.4957255 8.1123716 7.2860417 7.5662712 7.8671614
## 165 4.2386774 3.6444850 3.9140884 3.5720106 3.7810368 3.8455353
## 166 4.2406371 4.0987623 4.3946658 4.0194289 4.2721897 4.3695599
## 167 6.4828440 6.0410199 6.7417157 5.8042205 6.1722469 6.4868372
## 168 3.9517703 4.0138136 4.2929804 4.0212265 4.2389925 4.3189196
## 169 4.3295222 3.9540706 4.2005845 3.8125308 4.0033543 4.1295614
## 170 4.3464690 3.8590245 4.1090579 3.7089543 3.8681031 4.0117669
## 171 4.1459716 3.8153752 3.7978708 3.7166041 3.7880678 3.8119255
## 172 4.2248133 3.6966543 3.8234707 3.5978685 3.7452584 3.7863715
## 173 3.1610987 2.4314341 2.6311452 2.3443845 2.5952574 2.6011996
## 174 3.3491579 2.5577131 3.2582057 2.4648483 2.8063513 3.0635189
## 175 2.8147217 2.2706768 3.1051073 2.4415057 2.8358259 3.0138882
## 176 3.1831064 3.1425028 4.4436609 3.4573224 3.9127378 4.2774874
## 177 2.6129424 2.3885879 3.4250448 2.6970969 3.0596668 3.3183026
## 178 3.1605896 2.5128387 3.5008959 2.5795472 3.0391743 3.3077669
## 179 3.6543420 3.0601593 3.9877157 2.9885390 3.3978405 3.7461548
## 180 3.8381218 3.4807610 4.6277532 3.5092807 4.0070863 4.3879758
## 181 4.8555696 4.2693937 5.0542427 4.0128517 4.3487640 4.7504065
## 182 3.1884731 2.8595111 3.8571689 2.9339040 3.4599669 3.7108344
## 183 4.4168889 3.7405991 4.5949948 3.5148635 3.9840581 4.3153841
## 184 3.8087661 3.0079817 3.8264067 2.8087880 3.3291745 3.5830509
## 185 3.0172351 2.2735030 2.5916614 2.1409453 2.5068350 2.5284025
## 186 2.8511381 2.3597380 3.1037475 2.3341595 2.7182312 2.9566668
## 187 5.3123429 5.0764237 6.1286938 4.9988461 5.4410862 5.8527222
## 188 4.4143326 4.2871352 5.2535188 4.4210658 4.7646023 5.0778042
## 189 4.2707317 4.3021883 5.3835510 4.5500393 4.9292459 5.2290419
## 190 4.8339450 4.6949690 5.7005176 4.7839273 5.1307674 5.4824801
## 191 4.9001862 4.9954273 6.0651693 5.1641933 5.5416624 5.8677513
## 192 4.5688226 4.5462861 5.5844398 4.7304298 5.0893458 5.3909423
## 193 5.1058189 5.0976830 6.2005719 5.2422760 5.6286223 5.9751672
## 194 4.9465087 5.0867822 6.1554048 5.3417482 5.6689151 5.9855399
## 195 4.7227745 4.8467426 5.8915849 5.1023351 5.4456111 5.7344617
## 196 7.0278492 6.9729584 7.9101311 6.9843625 7.3365340 7.6760738
## 197 6.5810038 6.4942378 7.3051327 6.5632216 6.8264819 7.1032867
## 198 6.2748991 6.2612214 6.9205464 6.3099347 6.5051715 6.7528490
## 199 6.5483848 6.4521046 7.1876949 6.4837356 6.7230715 6.9895265
## 25 26 27 28 29 30
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20
## 21
## 22
## 23
## 24
## 25
## 26 1.1534378
## 27 0.3913349 0.9601190
## 28 1.0108345 0.6641659 0.9385630
## 29 0.9995264 1.7573289 1.0523239 1.3384639
## 30 1.3924842 2.0152347 1.3949992 1.5713712 0.4898614
## 31 1.0564778 1.1217431 1.2207035 1.1077362 1.9004252 2.2368968
## 32 0.6037321 1.2718750 0.6576296 1.0614166 0.7875682 1.2096483
## 33 2.4472033 1.8403745 2.4773802 1.7161003 2.9023792 3.0495131
## 34 0.7046486 0.8206851 0.8166324 0.8817912 1.5550316 1.9046474
## 35 1.7614146 1.1956323 1.7656626 0.9001024 2.0461423 2.2301084
## 36 1.7412560 2.0238046 1.6178847 2.0255673 1.7125466 1.7012390
## 37 1.8117644 1.9205585 1.6593397 1.9631248 1.8803837 1.8427786
## 38 2.4416296 2.5352724 2.2534003 2.6033366 2.4075718 2.2884205
## 39 2.8110515 2.8887636 2.6364328 2.9077325 2.7231570 2.5239326
## 40 5.1747672 5.3079272 5.0355235 5.2204924 4.8586586 4.6420737
## 41 5.6865250 5.8612216 5.5512612 5.7170884 5.2520847 4.9780207
## 42 4.3878202 4.4804357 4.2160452 4.3663273 4.0020694 3.7121064
## 43 4.0446615 4.0451178 3.8373808 4.0515567 3.8375044 3.6192552
## 44 3.9572828 3.9901501 3.7683066 3.9816574 3.7696981 3.5581815
## 45 2.8799827 2.9682074 2.6975102 2.9584837 2.7679517 2.6624786
## 46 2.9333440 2.9286092 2.7472441 3.0470821 3.0191043 2.9669867
## 47 2.8339012 2.8504768 2.6887803 2.9179440 2.9657652 2.9125550
## 48 1.8765272 2.1824737 1.8947483 2.0581878 2.1270887 2.3190899
## 49 2.8441632 2.9337574 2.9523788 2.9714701 3.5129477 3.7913446
## 50 2.2848111 2.3696537 2.1493557 2.4627463 2.5856542 2.6868696
## 51 3.1969285 3.2760838 3.0593180 3.2761777 3.2319425 3.2229475
## 52 3.0671545 3.2430600 2.9189403 3.1956934 2.9428937 2.9361959
## 53 4.2134994 4.3330756 4.0380586 4.2552489 3.9063196 3.7117571
## 54 3.9394672 3.9726606 3.7504437 3.9976616 3.8405690 3.7208683
## 55 4.2071905 4.2576955 4.1064529 4.2691514 4.2808219 4.3012193
## 56 6.4102572 6.5921303 6.2822015 6.4215875 6.0073348 5.7975967
## 57 5.6306322 5.7264412 5.4838159 5.6775679 5.4335061 5.3535541
## 58 6.5454539 6.6954808 6.4246073 6.5847698 6.2422211 6.1074446
## 59 3.6013719 3.6660056 3.3785541 3.6558450 3.4075123 3.2832935
## 60 2.8054929 2.9025287 2.5988340 2.9339099 2.7573785 2.7353198
## 61 2.3736254 2.4961859 2.1959078 2.5504450 2.5241458 2.6329075
## 62 1.9747296 2.2110509 1.8892687 2.1381474 2.1060630 2.3360046
## 63 2.8344970 3.1367598 2.6662034 2.9868228 2.4507477 2.3788981
## 64 3.4620540 3.7038390 3.3102277 3.5062620 3.0728286 2.9024112
## 65 4.3213163 4.6314090 4.1846941 4.3766330 3.8162592 3.6283338
## 66 5.5662817 5.6208827 5.4249851 5.6038504 5.3873569 5.2626498
## 67 5.0904302 5.0923791 4.9682270 5.1448050 5.1129379 5.0841175
## 68 3.4765988 3.4829009 3.2604431 3.5479167 3.4130774 3.2976237
## 69 2.8658279 2.8281230 2.6795780 2.9659413 3.0677615 3.0923103
## 70 3.1242796 3.1662487 2.9135291 3.2218992 3.0768586 2.9976236
## 71 3.8772009 3.9153470 3.6940802 3.8636206 3.6104359 3.3591173
## 72 3.2986926 3.2456935 3.0999828 3.2919388 3.2433566 3.0880612
## 73 3.8108894 3.8068806 3.6031495 3.8445239 3.6438681 3.4443725
## 74 3.7957473 3.7799113 3.6027278 3.7679230 3.6005340 3.3752896
## 75 3.9172990 3.9630136 3.7513875 3.9447416 3.7066322 3.4654406
## 76 2.7297255 2.8754237 2.5822783 2.7920290 2.4973515 2.3312167
## 77 2.0202143 2.2880879 1.9507207 2.1188223 1.8345601 1.7941889
## 78 2.6011348 2.7320014 2.4667151 2.6869460 2.4752082 2.3433289
## 79 2.3853620 2.5769148 2.2621515 2.4693141 2.2507270 2.1531750
## 80 2.8503789 2.9077705 2.6766836 2.9674045 2.8255837 2.7251681
## 81 3.6821750 3.9093867 3.5265509 3.7497965 3.2238207 2.9419062
## 82 2.7459984 3.1140266 2.6321921 2.9003396 2.2652647 2.1082158
## 83 3.3687128 3.5136276 3.1909253 3.4539412 3.0943681 2.8921528
## 84 2.9195703 3.0710739 2.7387796 3.0279057 2.6975404 2.5601854
## 85 2.6825206 2.9322582 2.5476036 2.7985585 2.3838375 2.1863752
## 86 2.9134264 3.2282227 2.7835868 3.0320530 2.4103331 2.1378724
## 87 2.4890466 2.6362051 2.3573743 2.6109882 2.4686586 2.3591063
## 88 2.4514327 2.6784726 2.3158505 2.6264030 2.2545731 2.1202627
## 89 2.9426894 3.4267974 2.9220443 3.1121441 2.2750005 2.0652392
## 90 3.3634733 3.7662430 3.3000335 3.4733239 2.7145674 2.3835169
## 91 2.5482871 2.8652985 2.4804972 2.7029348 2.2162189 2.0479906
## 92 2.4671495 2.8219481 2.4082421 2.6552398 2.1176963 1.9838330
## 93 3.0418520 3.2866163 2.9490690 3.1562261 2.7392255 2.5623383
## 94 3.6446581 3.7595162 3.4969670 3.7309132 3.4179564 3.2062789
## 95 2.4966237 2.8214399 2.4553185 2.6943404 2.3242495 2.2906615
## 96 3.1632821 3.3637911 3.0367170 3.1724634 2.6844646 2.3955883
## 97 2.2760961 2.5592360 2.2096695 2.4553233 2.1446538 2.0790294
## 98 4.7260374 5.2167479 4.7065371 4.7987000 3.9018076 3.5207880
## 99 5.2361720 5.5925401 5.1550338 5.2688479 4.5256102 4.0978951
## 100 3.8553787 4.2848223 3.8082161 3.9396681 3.1479139 2.7775761
## 101 2.2389809 2.7723157 2.2169286 2.4466342 1.5730131 1.2130324
## 102 2.4090991 2.8905817 2.3584014 2.5881898 1.7239502 1.3380369
## 103 3.8412676 3.1124367 3.6739440 2.9852305 3.6355846 3.5393053
## 104 1.1691497 1.7476182 1.2292378 1.5555300 1.1327773 1.2119579
## 105 1.3525926 1.9029771 1.3993122 1.7116831 1.2139584 1.2521553
## 106 1.2815208 1.7718248 1.4123850 1.6898627 1.6218261 1.7932580
## 107 1.2836621 1.7429745 1.4384443 1.6588144 1.7247142 1.8889855
## 108 1.4083744 1.8753167 1.4699988 1.6968764 1.3947634 1.4079977
## 109 1.5102094 2.1612724 1.6211665 1.8366573 1.1066225 1.1161907
## 110 1.1885758 1.7949139 1.3280558 1.5253549 1.1813208 1.2733628
## 111 1.9084344 2.1871136 1.8441734 2.0652329 1.7963624 1.6193807
## 112 2.5217892 2.9796077 2.5382258 2.6951804 2.0648878 1.8986347
## 113 1.9851606 2.3294934 2.0636227 2.2543932 2.1895784 2.3080345
## 114 1.9572617 2.3730660 2.0713279 2.2173665 2.0961401 2.2131302
## 115 2.2421706 2.5845303 2.2520607 2.4432244 2.0785921 2.0645288
## 116 2.0364468 2.1076180 2.0466016 2.0413320 2.2048159 2.2875615
## 117 2.2239438 2.5359039 2.1979301 2.4176545 2.1126220 2.0473213
## 118 2.1292213 2.4471182 2.0962439 2.3872827 2.0728516 2.0950577
## 119 2.2203537 2.1866379 2.1681228 2.1674513 2.3627357 2.3606439
## 120 2.2167592 2.3513584 2.1573862 2.4087730 2.4091523 2.4271303
## 121 3.2144084 3.3599619 3.1957530 3.3460991 3.2911914 3.2717765
## 122 3.0964654 3.2726623 3.1081924 3.2107288 3.1383830 3.1554856
## 123 3.0915984 3.2863222 3.1497371 3.2081694 3.2256286 3.2858050
## 124 3.3299976 3.4529613 3.4557668 3.3795482 3.6613625 3.7888912
## 125 3.0755479 3.2587000 3.1381875 3.2067847 3.2498720 3.3395661
## 126 3.1280980 3.3435953 3.1549148 3.2759371 3.1784153 3.2004563
## 127 3.5002773 3.5242707 3.6203344 3.5151172 3.9343747 4.0863603
## 128 2.6164007 2.8189439 2.6968782 2.8291788 2.9192087 3.0659288
## 129 2.7050007 3.1048181 2.8236015 2.8894293 2.6314223 2.6757769
## 130 2.6003435 2.7881463 2.6945927 2.8184827 2.9756326 3.1507577
## 131 2.7158132 3.1239701 2.7939738 2.9117811 2.5392065 2.5549800
## 132 2.6551149 3.0475447 2.7148218 2.8729142 2.5205575 2.5466145
## 133 2.7834031 3.1548604 2.8086371 2.9675063 2.5582517 2.5278155
## 134 2.4829314 2.7271783 2.5230078 2.6994193 2.6606086 2.7762412
## 135 2.8809676 2.5833310 2.8617175 2.5875773 3.1096447 3.2242640
## 136 2.6075474 2.9862226 2.7292173 2.7851113 2.6128732 2.6812607
## 137 2.5663329 2.7758758 2.6411526 2.7062691 2.7464876 2.8467886
## 138 2.7048306 3.0933286 2.8171509 2.8782328 2.6105673 2.6560228
## 139 2.7284656 2.9425973 2.8795528 2.8877014 3.0824493 3.2556894
## 140 2.6694647 3.0051403 2.8018039 2.8575853 2.7964072 2.8875405
## 141 2.8810185 3.1231619 3.0636803 2.9659265 3.1569324 3.2843762
## 142 3.9128488 3.9375477 4.0730223 4.0329271 4.5870306 4.8073196
## 143 6.3555919 6.4120320 6.4377053 6.4360375 6.6529642 6.7711414
## 144 4.9481043 5.0376103 5.0475964 5.0528075 5.2913591 5.4215882
## 145 5.2547955 5.2482916 5.3474628 5.3608625 5.7518933 5.9310523
## 146 5.5252070 5.2275568 5.5678386 5.1420095 5.6988846 5.7571136
## 147 5.2959404 4.9262930 5.2508933 4.9592486 5.4313940 5.4832522
## 148 5.2243421 5.2160045 5.3082027 5.3210779 5.7053088 5.8676276
## 149 5.0889399 5.0489484 5.1554509 5.1122677 5.4882801 5.6110770
## 150 4.7660421 4.7666865 4.8194403 4.7823710 5.0194915 5.1180208
## 151 4.7175468 4.8751012 4.7461715 4.7984816 4.7049775 4.7160357
## 152 4.7878829 4.7747122 4.7714905 4.8400988 4.9427140 5.0134621
## 153 6.2841367 6.2022309 6.2514047 6.3267857 6.4838765 6.5611356
## 154 4.8996064 4.7414500 4.8772388 4.7488115 5.0042778 5.0441845
## 155 6.1416989 6.1556454 6.1574326 6.1033444 6.1597275 6.1843337
## 156 6.9714613 6.5859986 6.9089194 6.5566022 6.9642272 6.9415851
## 157 5.7992377 5.2340232 5.7098755 5.3421860 5.9898665 6.0500266
## 158 5.1076140 5.4172506 5.0627753 5.1950493 4.6295991 4.4080959
## 159 4.0726265 4.2239409 4.0306188 4.1674368 3.9146981 3.8832657
## 160 4.9518335 5.1516442 4.9499873 5.0243486 4.7377029 4.6894236
## 161 5.7759365 5.8729015 5.7311916 5.8070882 5.5990742 5.5334722
## 162 6.0359979 6.3938586 5.9850881 6.1218259 5.4375096 5.1431081
## 163 7.3420280 7.6973693 7.3192674 7.4297505 6.8085497 6.5715845
## 164 7.6174512 7.9996177 7.6137461 7.6745579 7.0243760 6.7627861
## 165 3.7244319 3.9302776 3.7133724 3.9072834 3.7381577 3.7598890
## 166 4.2168647 4.0543073 4.1268910 3.9891955 4.0833872 4.0217844
## 167 6.2063434 6.5976778 6.1839802 6.2630922 5.5579095 5.2546051
## 168 4.1914322 3.9107600 4.0835940 3.9054469 4.1672556 4.1143852
## 169 3.9908238 4.0154724 3.9582702 3.8895188 3.8289544 3.7769913
## 170 3.8687408 3.9883573 3.8604387 3.8430752 3.6994527 3.6591716
## 171 3.7634403 3.6537129 3.7380014 3.6351286 3.8460315 3.9015343
## 172 3.6933902 3.7676982 3.6795249 3.7447381 3.7282528 3.7796529
## 173 2.5115017 2.7336572 2.4933024 2.7811979 2.7307168 2.8056927
## 174 2.7690998 3.1442156 2.7495121 2.9685042 2.4608884 2.3601503
## 175 2.7367651 2.9244044 2.6506038 2.9350185 2.7058840 2.6544512
## 176 3.8759283 4.0599867 3.7482131 3.9452140 3.4980699 3.2102565
## 177 2.9930060 3.1265942 2.8748352 3.1124507 2.9047297 2.7786702
## 178 2.9335370 3.2422883 2.8425320 3.1253116 2.6029294 2.4671585
## 179 3.3872548 3.7739122 3.3387341 3.5173253 2.8496575 2.5888413
## 180 3.9950170 4.3568024 3.9097815 4.1128704 3.4075154 3.0515233
## 181 4.4258636 4.9221993 4.4269335 4.5179508 3.6848883 3.3265782
## 182 3.4037712 3.6764453 3.2989707 3.5813059 3.1376715 2.8983986
## 183 3.9650522 4.4342616 3.9276125 4.1240883 3.2961472 2.9960139
## 184 3.2396758 3.6826634 3.1839191 3.4702040 2.7352345 2.5420886
## 185 2.3873039 2.6333173 2.3325410 2.6615942 2.5374591 2.5798716
## 186 2.6923018 2.9672621 2.6187408 2.8429260 2.5288116 2.3738951
## 187 5.4808035 5.8733736 5.4129400 5.5382471 4.7729539 4.3589955
## 188 4.7492176 4.9635322 4.6594244 4.8092718 4.3838423 4.1487705
## 189 4.8671597 4.9887701 4.7339849 4.8993162 4.5499997 4.3321622
## 190 5.1236091 5.3843198 5.0335171 5.1715203 4.6475827 4.3731096
## 191 5.4873908 5.6386174 5.3416764 5.4851908 5.0753066 4.8117324
## 192 5.0088923 5.1666421 4.8667211 5.0439797 4.6488882 4.4424535
## 193 5.5727997 5.7803984 5.4372573 5.5971230 5.0919429 4.8199807
## 194 5.6198302 5.7386925 5.4826527 5.6309260 5.2914481 5.0655369
## 195 5.3684635 5.4463260 5.2186303 5.3663162 5.0696769 4.8718323
## 196 7.3362951 7.6069002 7.2458742 7.3603509 6.7982446 6.4969834
## 197 6.7833613 6.9760016 6.6865998 6.8077883 6.4022105 6.2189775
## 198 6.4798470 6.5854410 6.3863457 6.4275825 6.1751403 6.0204942
## 199 6.6934111 6.8886214 6.6053634 6.7100070 6.3291663 6.1500824
## 31 32 33 34 35 36
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20
## 21
## 22
## 23
## 24
## 25
## 26
## 27
## 28
## 29
## 30
## 31
## 32 1.4730434
## 33 1.6674343 2.6794356
## 34 0.6344059 0.9796073 1.9942363
## 35 1.4034469 1.7574336 1.1965885 1.3664254
## 36 2.4429101 1.7125927 3.3612560 2.0162039 2.7074395
## 37 2.3727840 1.8733081 3.1449862 2.0033298 2.6076942 0.4398399
## 38 3.0394482 2.5111938 3.7487395 2.7085017 3.3045509 1.0277743
## 39 3.3405956 2.9309363 3.8839634 3.0759759 3.5607437 1.5104245
## 40 5.7064531 5.1768201 6.0794468 5.4956760 5.7383414 4.2358416
## 41 6.2727858 5.6566120 6.6006741 6.0491613 6.2293048 4.7080229
## 42 4.9709869 4.4040443 5.2941909 4.7527062 4.9855667 3.1518686
## 43 4.5779479 4.1095672 4.9723067 4.3555452 4.6973168 2.7675248
## 44 4.4655506 4.0503079 4.8665971 4.2705577 4.6300247 2.7231301
## 45 3.4134222 2.9636787 4.0021403 3.2012637 3.6398662 1.7516393
## 46 3.3692605 3.0693646 3.9939386 3.1542875 3.7089542 1.7355795
## 47 3.1530332 3.0519272 3.6916259 3.0324129 3.5389226 1.8360015
## 48 2.0659668 2.1043948 2.8913507 2.0831851 2.5676922 2.0042303
## 49 2.2860058 3.2775879 2.8264286 2.7027215 3.1171299 3.5525974
## 50 2.5494906 2.5558855 3.3081484 2.4951064 3.0932663 1.8670040
## 51 3.5430961 3.3593397 4.0914780 3.4667500 3.8792355 2.4468837
## 52 3.5925082 3.1023097 4.2688464 3.4148039 3.8248394 2.2789796
## 53 4.7904733 4.2374116 5.2415440 4.5917885 4.8968507 3.0587645
## 54 4.4031750 4.0479376 4.8787767 4.2471643 4.6391652 2.8465423
## 55 4.4306665 4.3579563 4.8768127 4.4070735 4.7442823 4.2066664
## 56 6.9195694 6.4215794 7.2020504 6.8008675 6.9208361 5.7301147
## 57 6.0684984 5.6622610 6.4873948 5.9569160 6.2055314 5.0478143
## 58 7.0114916 6.5354116 7.3632664 6.8764729 7.0394530 5.8036707
## 59 4.1675225 3.6745041 4.7025691 3.9932857 4.3734201 2.8930021
## 60 3.3512914 2.8997794 4.0498021 3.1639727 3.6686678 2.2221315
## 61 2.7945684 2.5497210 3.5969848 2.6942396 3.2513455 2.2759961
## 62 2.3649801 2.0512826 3.2471272 2.2681704 2.7266400 2.3624920
## 63 3.5584320 2.7797879 4.2957923 3.3226961 3.7036020 2.3910743
## 64 4.0532463 3.5151438 4.5425989 3.9323859 4.1831603 2.9863582
## 65 4.9387431 4.3289417 5.3872254 4.8309164 4.9739914 3.8494880
## 66 6.0018676 5.5883740 6.3856720 5.8332422 6.1114914 4.6303952
## 67 5.3725186 5.1834190 5.7827007 5.2707485 5.6079856 4.3616039
## 68 3.9760172 3.5932369 4.5127863 3.7878292 4.2473311 2.4959608
## 69 3.1856970 3.0819689 3.8109216 3.0845189 3.6412110 2.2424730
## 70 3.6397939 3.2357634 4.2482400 3.4476996 3.9352173 2.2199431
## 71 4.4174252 3.9318503 4.7787286 4.1968937 4.5005879 2.7772703
## 72 3.7368358 3.4246746 4.1527326 3.5447606 3.9345021 2.3048059
## 73 4.3545682 3.8708204 4.8100212 4.1058893 4.5115856 2.6623327
## 74 4.2929347 3.8727412 4.6420236 4.0821673 4.3989749 2.7110361
## 75 4.4379497 3.9767844 4.8328223 4.1948137 4.5553627 2.7607994
## 76 3.3191448 2.7411935 3.8890527 3.0433454 3.4291370 1.7815768
## 77 2.5852630 1.9934201 3.2811936 2.2991227 2.6777173 1.5567568
## 78 3.1362950 2.6519518 3.7307617 2.8667779 3.3077170 1.6560899
## 79 2.9017465 2.4800919 3.5099908 2.7047234 3.1120101 1.7660033
## 80 3.3657272 2.9335545 3.9936104 3.1006113 3.6260911 1.8526740
## 81 4.3629369 3.6582204 4.8517340 4.1039503 4.3915186 2.5857289
## 82 3.4866232 2.6485107 4.1849858 3.1991723 3.5394961 1.9764096
## 83 3.9861045 3.3979782 4.5291023 3.7345865 4.1225260 2.2421406
## 84 3.5457741 2.9346375 4.1762714 3.2769903 3.7045438 1.8742767
## 85 3.3145137 2.7185822 3.9204607 3.0625805 3.4621973 1.4530768
## 86 3.6564083 2.8352585 4.2636095 3.3384409 3.6629887 1.6595635
## 87 2.9555449 2.6449681 3.5623767 2.7566681 3.2482167 1.3118120
## 88 3.1069939 2.4344579 3.8279612 2.7613592 3.2661838 0.9242053
## 89 3.7246627 2.6909216 4.4174527 3.3544950 3.6048504 2.0099682
## 90 4.1086597 3.2172843 4.6494417 3.7815589 3.9940441 2.1966475
## 91 3.2020859 2.4645561 3.8744820 2.8536728 3.2478992 1.1666171
## 92 3.1554759 2.3388935 3.8905456 2.7808707 3.1953288 1.1626582
## 93 3.6443583 2.9998556 4.2320308 3.3475612 3.7096579 2.1362426
## 94 4.2132313 3.6533871 4.7174090 3.9212974 4.3113304 2.5132990
## 95 3.0578046 2.4486436 3.8053270 2.7620570 3.2032948 1.9711858
## 96 3.8241743 3.0586514 4.2767279 3.4925582 3.6771706 1.8393115
## 97 2.8359084 2.2784966 3.5625164 2.5349736 3.0049815 1.0432911
## 98 5.4603964 4.5461950 5.8489374 5.1891609 5.1939967 3.9227672
## 99 5.9300722 5.1496371 6.2104649 5.6743206 5.7224979 4.1665768
## 100 4.5738856 3.7282626 5.0197414 4.2910248 4.4125901 2.8284493
## 101 3.0363381 2.0939737 3.7369843 2.6619670 2.9830328 1.8931136
## 102 3.2300186 2.2435115 3.9064923 2.8382568 3.1610313 1.8626975
## 103 3.8879427 3.5756874 3.2058173 3.6220111 2.6117806 3.8571704
## 104 1.8723175 1.1281542 2.8847670 1.4357478 2.1299116 1.4508236
## 105 2.0705098 1.2334551 3.0464313 1.6081548 2.2427640 1.4992761
## 106 1.6592839 1.3826241 2.7275687 1.2864049 2.0705138 1.8664506
## 107 1.4918057 1.5147217 2.5301231 1.2344093 2.0188614 1.9475618
## 108 1.9822198 1.3973154 2.8762359 1.5703866 2.1727074 1.5446678
## 109 2.2398296 1.2959624 3.1666487 1.8195813 2.3032101 1.7786626
## 110 1.7537641 1.2030972 2.7161619 1.3938665 1.9995796 1.6909294
## 111 2.4701053 2.0036774 3.1450927 2.1567066 2.6795001 1.3954882
## 112 3.1701924 2.3831675 3.8446418 2.8390718 3.1451308 1.8789984
## 113 2.2687066 2.0511240 3.1261583 2.0182785 2.5842942 1.9004795
## 114 2.2350287 2.0220807 3.0709657 2.0278441 2.5306064 1.9967172
## 115 2.8052172 2.1066726 3.5859486 2.4193306 2.8706581 1.6136195
## 116 2.2451235 2.0500775 2.8433168 1.9782180 2.2871956 1.8749994
## 117 2.7543627 2.2177921 3.4835110 2.4350522 2.9112112 1.4769837
## 118 2.7102550 2.0447107 3.5724328 2.3217941 2.8849200 1.4652931
## 119 2.4425286 2.2857121 2.9095292 2.1877463 2.4720413 1.7487480
## 120 2.5774616 2.3256562 3.3244199 2.2948041 2.8994553 1.5031436
## 121 3.4816246 3.2839946 4.0278448 3.2772881 3.6721821 3.1603660
## 122 3.3617576 3.1038472 3.9238334 3.1428569 3.4723445 3.2040036
## 123 3.2154074 3.1562426 3.7428165 3.0787951 3.3774504 3.4198506
## 124 3.1044018 3.5099251 3.4376948 3.1636665 3.3649845 3.9533475
## 125 3.1849862 3.1268336 3.7552802 3.0357304 3.3671481 3.4339865
## 126 3.3865625 3.1438682 3.9740594 3.1741449 3.5215812 3.2710984
## 127 3.1494436 3.7114315 3.4027393 3.2502086 3.4419689 4.1518610
## 128 2.7158969 2.6802531 3.4629984 2.5215183 3.0272962 3.3385333
## 129 3.0144660 2.6475101 3.6835410 2.7906745 3.1064146 3.3429404
## 130 2.6224596 2.6981513 3.3856925 2.4716239 3.0101551 3.3947498
## 131 3.1540359 2.5976223 3.8636780 2.8695624 3.1958332 3.2505800
## 132 3.1045884 2.5485198 3.8522408 2.8091948 3.1860374 3.1832848
## 133 3.2877688 2.6595644 3.9787297 2.9749077 3.2870225 3.2098680
## 134 2.7409443 2.5038457 3.5161429 2.5014782 2.9874693 3.1641345
## 135 2.7908216 2.8394194 2.9148544 2.6195923 2.4739711 3.6314284
## 136 2.8474358 2.6035382 3.5085874 2.6693212 2.9936477 3.3417212
## 137 2.7170853 2.6009335 3.3648437 2.5206803 2.9015774 3.2616446
## 138 3.0366284 2.6203611 3.7090198 2.7938684 3.1030773 3.3210814
## 139 2.6242101 2.8446413 3.2563552 2.5618658 2.9662274 3.6228364
## 140 2.8055920 2.7145497 3.4588993 2.6542813 3.0194905 3.4183287
## 141 2.7059813 3.0305675 3.1447853 2.7347541 2.9823744 3.7852046
## 142 3.2993216 4.2556456 3.5972399 3.5557875 3.9100017 4.9362891
## 143 6.1706949 6.4751382 6.4243028 6.2107914 6.4174142 6.6071574
## 144 4.7404328 5.0971716 5.0657802 4.7855548 5.0406988 5.2462861
## 145 4.9149546 5.4557123 5.2243829 5.0065913 5.3212136 5.6138895
## 146 5.1768278 5.5534558 4.7175327 5.2379194 4.7830230 5.8439705
## 147 5.1718186 5.2230571 4.9799012 5.0500018 4.7442679 5.3570315
## 148 4.8949288 5.4371964 5.1756045 4.9910429 5.2874284 5.5634326
## 149 4.7984882 5.2752762 4.9693068 4.8747170 5.0544543 5.3768739
## 150 4.6562861 4.8388111 4.9227157 4.6163516 4.7801605 4.9191398
## 151 4.9085595 4.6838019 5.3174377 4.7420584 4.9254978 4.6370117
## 152 4.8954077 4.7655840 5.3054685 4.7098543 4.9344534 4.7235986
## 153 6.3409166 6.2806017 6.6887542 6.1874846 6.4277905 6.1760747
## 154 4.9007070 4.8584402 4.9921228 4.7594507 4.6930418 4.9019232
## 155 6.2122864 6.1016679 6.4036759 6.1000573 6.1297854 6.1308097
## 156 6.8912688 6.8723071 6.5085650 6.7864315 6.3454789 6.9177496
## 157 5.5977377 5.7196167 5.2182614 5.4810016 5.0567283 5.8415344
## 158 5.6817956 4.9567685 6.0905831 5.3844646 5.4558948 4.4576941
## 159 4.5080975 3.9107481 5.0579650 4.1742229 4.3989500 3.5110640
## 160 5.3306938 4.8064925 5.7783064 5.0708711 5.2095728 4.7029062
## 161 6.1279199 5.6535278 6.4892209 5.8737616 5.9850120 5.3091739
## 162 6.6703093 5.8820613 7.0281758 6.3802512 6.4086279 5.3277917
## 163 7.8937702 7.2015482 8.2201581 7.6534430 7.6671704 6.8124436
## 164 8.1595671 7.4762616 8.4175902 7.9458968 7.8940911 7.1163756
## 165 4.0507266 3.6985847 4.6823862 3.8142437 4.1894797 3.2961703
## 166 4.4556033 4.0706733 4.5546257 4.1945986 4.0250096 3.7727139
## 167 6.8136465 6.0472068 7.1079557 6.5567444 6.5060107 5.6006888
## 168 4.3253305 4.1161691 4.3105426 4.1104740 3.9292872 3.7252928
## 169 4.2710357 3.8605694 4.5279058 4.0244912 3.9829644 3.5872998
## 170 4.1805184 3.7483880 4.5418947 3.9410804 3.9926959 3.4756468
## 171 3.8514636 3.7039532 4.0962330 3.6674927 3.6778719 3.5387956
## 172 3.9330403 3.6200898 4.4328653 3.6978616 3.9200181 3.3748970
## 173 2.8154550 2.6065176 3.6174062 2.5694442 3.1474455 1.7763983
## 174 3.3810682 2.6465529 4.0908564 3.0366205 3.4053281 1.6477295
## 175 3.2475042 2.7269753 3.9676771 2.9092131 3.4215718 1.3459793
## 176 4.4957315 3.8402714 4.9418687 4.1888165 4.4809167 2.3548774
## 177 3.4844467 3.0480471 4.0643107 3.2186135 3.6629137 1.5307719
## 178 3.6170021 2.8116384 4.3327325 3.2494194 3.6556051 1.5744152
## 179 4.0691949 3.2543298 4.6249147 3.7458164 3.9673339 2.2263249
## 180 4.7066350 3.8997850 5.1800999 4.3897066 4.5922522 2.7905789
## 181 5.0979899 4.2860296 5.4855075 4.8441215 4.8632475 3.6641197
## 182 3.9859240 3.4340546 4.5376154 3.6950620 4.0564275 2.1923997
## 183 4.7045790 3.7850101 5.2549766 4.3717086 4.5192711 3.0955590
## 184 3.9814322 3.0660101 4.6902387 3.6081654 3.9142321 2.3047593
## 185 2.7801228 2.4814730 3.5864897 2.5159928 3.0741675 1.6946191
## 186 3.1878554 2.7714887 3.7642157 2.9541029 3.3172995 1.6436885
## 187 6.1624026 5.3968118 6.4474284 5.9159274 5.9409646 4.5327444
## 188 5.2785745 4.7263198 5.6525381 5.0521880 5.2532035 3.5624475
## 189 5.3985996 4.8466165 5.7690039 5.1616444 5.3885305 3.6114574
## 190 5.7013147 5.0820827 6.0449108 5.4868808 5.6308235 4.0038228
## 191 6.0304926 5.4970126 6.3048099 5.8571234 5.9900751 4.4081024
## 192 5.5603601 5.0012986 5.9427604 5.3686509 5.5771660 3.9265158
## 193 6.1741741 5.5414473 6.5022330 5.9747708 6.1160464 4.4879151
## 194 6.1181127 5.6418166 6.4141891 5.9486543 6.1427719 4.5114286
## 195 5.8641766 5.3709941 6.1808388 5.6761766 5.8706893 4.2634855
## 196 7.8967158 7.2985773 8.1157028 7.7251976 7.7587006 6.3711789
## 197 7.2646605 6.7579532 7.5596990 7.1232195 7.2354800 5.8413773
## 198 6.8499399 6.4835361 7.0262664 6.7558382 6.7878696 5.6305173
## 199 7.1396769 6.6889234 7.4041356 7.0241925 7.1145466 5.8090780
## 37 38 39 40 41 42
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
## 16
## 17
## 18
## 19
## 20
## 21
## 22
## 23
## 24
## 25
## 26
## 27
## 28
## 29
## 30
## 31
## 32
## 33
## 34
## 35
## 36
## 37
## 38 0.8735678
## 39 1.2780680 0.6243352
## 40 4.1974105 3.8449661 3.7011002
## 41 4.6851227 4.2964738 4.0948048 0.8510830
## 42 3.0618459 2.3885275 2.0836491 3.3931602 3.4788406
## 43 2.6263737 1.8911401 1.6313090 3.4427789 3.7090611 0.8876224
## 44 2.5738067 1.8514851 1.5700007 3.4640280 3.7466208 0.9134614
## 45 1.6503699 1.2409068 1.3373524 3.6583292 4.0875575 1.8746120
## 46 1.5688941 1.1019857 1.2573337 3.8582391 4.3628251 2.2138325
## 47 1.6014756 1.2962120 1.3084754 3.9418915 4.4488365 2.3334703
## 48 1.9865979 2.4715369 2.7538300 4.7994268 5.3301923 3.8380425
## 49 3.4269216 3.9562478 4.1551637 6.1202410 6.7375355 5.4395750
## 50 1.7240064 1.8747440 2.1055728 4.3816739 4.9450424 3.2189054
## 51 2.3442324 2.1766698 2.2738181 3.3304212 3.8974818 2.6562733
## 52 2.3022023 2.2311983 2.4445525 3.2933285 3.8073634 2.7722360
## 53 3.0114750 2.4654292 2.3504962 2.6270368 2.9002449 1.4140908
## 54 2.7308567 2.2056047 2.1290352 2.8585715 3.3199191 1.8505824
## 55 4.1400933 4.0628480 4.1288755 3.1446651 3.7878973 4.7021883
## 56 5.7077093 5.3701289 5.2104766 2.0506326 1.8421016 4.4306886
## 57 5.0350774 4.7499243 4.7516374 2.1723370 2.5974563 4.3545040
## 58 5.8077759 5.5721469 5.5185886 2.4381013 2.5409197 4.9527930
## 59 2.8257975 2.3230261 2.3117494 2.8487737 3.2701931 2.2794592
## 60 2.1801980 1.8976648 2.0816433 3.1190345 3.6788328 2.7475858
## 61 2.2357152 2.2738378 2.5319535 3.6747204 4.2857823 3.4851597
## 62 2.4201710 2.7867079 3.1326469 4.2293306 4.8117116 4.1701936
## 63 2.4864360 2.3775502 2.5769464 3.1585557 3.5628526 2.9447645
## 64 2.9674582 2.6601902 2.6192617 2.9322219 3.2244044 2.4538631
## 65 3.8703396 3.6614800 3.5935111 3.4856163 3.5621925 3.0219266
## 66 4.5930948 4.2392765 4.1932726 1.6089047 2.1265528 3.7894165
## 67 4.2952364 4.0846128 4.1198825 2.3243993 3.0529928 4.2005072
## 68 2.3660045 1.7581451 1.7154117 3.2122140 3.6718852 1.9329177
## 69 2.0831505 1.7996581 1.9492783 3.7451370 4.3383370 2.7969315
## 70 2.1172972 1.6287223 1.7004980 3.2880517 3.7827462 2.1577193
## 71 2.6488368 1.9781813 1.7066186 3.5998951 3.8239755 1.1918587
## 72 2.1098353 1.5265133 1.3780802 3.7978173 4.1924811 1.8434828
## 73 2.5360741 1.8102988 1.6335944 3.6827251 3.9851680 1.4945217
## 74 2.5527396 1.8798500 1.6196038 3.6613875 3.9389029 1.3628489
## 75 2.6305592 2.0020908 1.7414252 3.8381382 4.0805959 1.7491241
## 76 1.7359412 1.5294587 1.6095859 3.9743109 4.3293299 2.3658974
## 77 1.5989618 1.9669076 2.2136332 4.4677696 4.8766402 3.3190705
## 78 1.5771422 1.4479722 1.5518054 4.0838597 4.4801740 2.5697887
## 79 1.6948864 1.6885048 1.7986180 4.1478612 4.5507964 2.7028306
## 80 1.7468386 1.3976114 1.5024250 4.0646938 4.4922021 2.4767769
## 81 2.5738700 2.1293292 1.9784653 2.2673036 2.4846012 1.6966207
## 82 2.0994980 2.1159431 2.2837261 2.9208120 3.2992189 2.7669961
## 83 2.1843753 1.6895713 1.6128450 2.3812653 2.8041783 1.8167679
## 84 1.8500106 1.5474886 1.6544576 2.6296749 3.1335420 2.2611308
## 85 1.4109969 1.1584379 1.1823829 3.5478547 3.9015042 1.9543196
## 86 1.7272163 1.5670766 1.5940272 3.5264974 3.7721509 2.0622718
## 87 1.1073881 0.9521111 0.9953423 3.7761154 4.2346979 2.3369665
## 88 0.9534773 0.9471173 1.2246366 3.7761027 4.1891492 2.4699374
## 89 2.2594887 2.5057561 2.7073260 4.2212708 4.4283764 3.2655992
## 90 2.3171440 2.2979445 2.2755181 3.7825382 3.8918432 2.5487566
## 91 1.2813436 1.5143158 1.7144052 3.9541955 4.3066524 2.7936479
## 92 1.3510685 1.6773917 1.9426708 4.0759456 4.4346474 3.0197709
## 93 2.1642623 2.1154428 2.1877223 3.2124479 3.5930389 2.7836990
## 94 2.4517239 2.0765537 1.9871052 2.9663531 3.3217812 2.3378274
## 95 2.0603499 2.3544804 2.5869803 3.7603988 4.2274165 3.5455925
## 96 1.8527549 1.8320453 1.8063398 3.6355145 3.8575594 2.3623984
## 97 1.0905830 1.4888372 1.7513494 4.0631542 4.5015309 3.0093014
## 98 4.0455667 4.0589451 3.9349055 4.4812571 4.2765743 3.6685390
## 99 4.1797281 3.9309561 3.6121895 4.0708484 3.7505591 2.9615735
## 100 2.9175823 2.8812234 2.7581522 3.8506625 3.8314993 2.7270173
## 101 2.0156083 2.3259724 2.4150479 4.4983772 4.7326698 3.6181466
## 102 1.9922143 2.1682767 2.2444887 4.3371351 4.5481595 3.3384078
## 103 3.7386253 4.1794522 4.3174030 5.9795484 6.2875859 5.2351853
## 104 1.5595274 2.1920666 2.4937371 4.9424183 5.3752316 4.1438024
## 105 1.6369227 2.2649786 2.5651834 4.9604230 5.3739402 4.1943341
## 106 1.9120830 2.6400905 2.9292024 5.3667925 5.8450569 4.7156562
## 107 1.9327462 2.6461481 2.8932522 5.3809815 5.8712477 4.7027387
## 108 1.6038532 2.2486831 2.5005073 4.9847750 5.4083892 4.2022288
## 109 1.9634765 2.5763046 2.8596649 5.0587945 5.4279262 4.3214695
## 110 1.7681886 2.4414672 2.7034623 5.0941899 5.5224970 4.3351704
## 111 1.3008877 1.5139362 1.5976559 4.4071830 4.7974236 3.2844384
## 112 2.0275261 2.3985835 2.5687013 4.6269260 4.9133860 3.6192669
## 113 1.9442755 2.6124101 2.8953161 5.2592255 5.7358851 4.4701548
## 114 2.0530950 2.7229346 2.9884001 5.2803338 5.7393426 4.4883940
## 115 1.7664866 2.2758223 2.5794568 4.8660870 5.2626757 3.9282579
## 116 1.8491415 2.5292544 2.8007940 5.1867590 5.6615535 4.3371998
## 117 1.5190800 1.9345377 2.1496469 4.6081874 5.0094817 3.5585865
## 118 1.6013523 2.0902907 2.4244986 4.7938519 5.2246606 3.8520350
## 119 1.6199982 2.1866065 2.3783862 4.9131044 5.3775998 3.9453648
## 120 1.4243256 1.8225320 2.0695816 4.7422748 5.2287482 3.6952957
## 121 3.1237118 3.3797959 3.4856031 5.6936127 6.0747382 4.6022917
## 122 3.2141260 3.5794866 3.7455321 5.8763420 6.2575874 4.8683646
## 123 3.4124236 3.8691548 4.0300245 6.1580916 6.5629724 5.2444349
## 124 3.8923172 4.4280535 4.5731223 6.7245169 7.1840714 5.8823600
## 125 3.4402495 3.9150854 4.1091575 6.2496307 6.6728942 5.3562546
## 126 3.2867225 3.6808232 3.8430028 5.9592215 6.3385847 5.0045261
## 127 4.0633422 4.6080819 4.7580091 6.9515579 7.4459296 6.1331396
## 128 3.3582307 3.8475852 4.0870787 6.4146040 6.8672656 5.6505145
## 129 3.4245549 3.8871978 4.0849667 6.2144702 6.5613950 5.4069122
## 130 3.4065507 3.8937782 4.1431667 6.4904278 6.9645622 5.7144381
## 131 3.3581830 3.7787257 3.9874579 6.0616481 6.3842027 5.2413351
## 132 3.2854145 3.6944148 3.9097364 6.0167344 6.3526915 5.1954177
## 133 3.3048134 3.6910365 3.8733729 5.9176761 6.2179910 5.1102009
## 134 3.2014729 3.6482868 3.8831681 6.1559212 6.5774421 5.3583656
## 135 3.5757979 4.1131548 4.3376406 6.5528631 6.9961471 5.7730992
## 136 3.3987198 3.8733983 4.0650471 6.2310225 6.5992435 5.4230011
## 137 3.2776212 3.7543950 3.9639934 6.2539502 6.6716170 5.4463218
## 138 3.4129012 3.8667665 4.0775928 6.1980099 6.5433460 5.3767620
## 139 3.6265103 4.1603902 4.3844627 6.6886791 7.1525566 5.9290118
## 140 3.4518596 3.9524486 4.1414925 6.3725292 6.7687150 5.5961993
## 141 3.7636073 4.2883004 4.4503555 6.7084590 7.1411632 5.9147219
## 142 4.8185586 5.3723066 5.5153051 7.8163157 8.3721927 7.2161674
## 143 6.5718806 6.9344725 7.0672998 8.8293194 9.2568036 8.1993182
## 144 5.2010899 5.6418576 5.7870754 7.8016782 8.2604259 7.0925004
## 145 5.5408518 5.9827488 6.1510889 8.2369863 8.7633916 7.5602981
## 146 5.7307699 6.2304985 6.3300665 8.1510178 8.5415381 7.3928687
## 147 5.2813504 5.7169612 5.8829255 7.7064748 8.0983493 6.9530452
## 148 5.4768474 5.9106251 6.0539966 8.1321094 8.6463378 7.4545187
## 149 5.2779137 5.7126167 5.8250726 7.8703031 8.3467138 7.1660889
## 150 4.8805706 5.2922869 5.4511412 7.4490867 7.8815792 6.6745625
## 151 4.6688635 5.0061849 5.1451405 6.9516046 7.2672855 6.1582965
## 152 4.7273818 5.0877209 5.2814085 7.1940274 7.5921224 6.4612271
## 153 6.1665311 6.3986978 6.5753166 8.2571484 8.6531386 7.5814543
## 154 4.8597282 5.2624984 5.4159951 7.2806612 7.6544731 6.5146723
## 155 6.1376085 6.4255360 6.5543618 8.0982919 8.4005281 7.3825602
## 156 6.8320723 7.1222638 7.2065233 8.6329171 8.9104728 7.8789580
## 157 5.7276620 6.1346736 6.3041407 8.0893229 8.5061050 7.3409994
## 158 4.5343456 4.7248674 4.7043084 5.8205294 5.8437690 5.0788257
## 159 3.6067235 3.9499391 4.1557914 5.8540075 6.1579960 5.0198583
## 160 4.7929934 5.0618897 5.2084292 6.7941075 7.0160382 5.9906174
## 161 5.3603095 5.5540137 5.6586957 6.9116817 7.1164509 6.2017807
## 162 5.4021019 5.4789697 5.3650782 6.0847240 5.9279133 5.4011979
## 163 6.8925373 6.9739262 6.8897652 7.4199595 7.2634413 6.8817344
## 164 7.1957761 7.2657170 7.1527517 7.5783130 7.3620746 7.0052748
## 165 3.3465184 3.6889304 3.8810674 5.7759653 6.1555471 4.8773044
## 166 3.7451587 4.1227219 4.2578934 5.9378194 6.2437311 5.0467847
## 167 5.6800684 5.7934443 5.6717178 6.3089355 6.1169202 5.6420164
## 168 3.6283683 3.9676511 4.0700682 5.8803057 6.2301768 4.9067113
## 169 3.6063731 4.0084634 4.1550642 5.8707608 6.1721415 4.9692832
## 170 3.5225547 3.9098128 4.0708297 5.8032860 6.1086333 4.8690664
## 171 3.5193300 3.9779996 4.1929699 6.1101174 6.5297923 5.2005189
## 172 3.4172816 3.8358918 4.0702250 5.9642858 6.3658822 5.0761124
## 173 1.7662843 2.3720601 2.6335491 4.8912624 5.3976893 4.1753187
## 174 1.8115546 2.2212405 2.4452467 4.3965765 4.7370863 3.4906701
## 175 1.3714148 1.6917672 1.9456882 4.2979494 4.7401805 3.2958128
## 176 2.3154319 1.9557050 1.7493367 3.6024976 3.7665662 1.9693130
## 177 1.4314712 1.3285439 1.3984538 3.8985752 4.3099157 2.5250897
## 178 1.7262533 1.9029115 2.1199894 4.0784845 4.4054867 3.0181122
## 179 2.3410425 2.4925684 2.5183147 4.0960157 4.2618739 3.0780619
## 180 2.8365305 2.7565439 2.5841368 3.8428973 3.8500667 2.7939755
## 181 3.7630017 3.8939259 3.7705077 4.5930410 4.4881142 3.8706563
## 182 2.1324720 2.2044660 2.0696218 3.9869133 4.2382559 3.0906248
## 183 3.2359290 3.4236029 3.4095698 4.4639065 4.4834466 3.8129906
## 184 2.4763284 2.7823517 2.9078083 4.3827018 4.5897399 3.7194496
## 185 1.6739316 2.2694912 2.4982603 4.6893741 5.1749231 4.0261501
## 186 1.5585066 1.8670473 1.8687388 4.0673887 4.4356125 3.1073134
## 187 4.5523080 4.4234819 4.1270109 4.5402835 4.2216800 3.7469421
## 188 3.5469911 3.3672036 3.2279063 2.4027672 2.5622573 3.1077418
## 189 3.5757783 3.2614516 3.1319422 2.1861735 2.4085174 2.8173088
## 190 4.0066366 3.7780170 3.5987088 2.4437454 2.3728712 3.1105411
## 191 4.3507132 3.9765553 3.7409464 2.3544931 2.2616806 2.9110781
## 192 3.9048940 3.5584757 3.4365554 2.2212435 2.3679765 2.8019737
## 193 4.4757209 4.1076797 3.9073089 2.4312457 2.2392467 2.9878194
## 194 4.4528741 4.0323582 3.8346623 1.5838340 1.6530074 2.9503516
## 195 4.2131793 3.8333070 3.6987432 1.5237703 1.7763464 2.9757759
## 196 6.3642559 6.1225503 5.8728417 3.3611090 2.8224192 5.0437005
## 197 5.8488140 5.6034046 5.4961845 3.0566790 2.9642591 4.6642360
## 198 5.5980791 5.4219711 5.3243700 3.0794948 3.1597461 4.6526562
## 199 5.8027241 5.5970197 5.4780759 3.1081328 3.0491487 4.7273310
## 43 44 45 46 47 48
## 2
## 3
## 4
## 5
## 6
## 7
## 8
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## 39
## 40
## 41
## 42
## 43
## 44 0.2733197
## 45 1.3804106 1.3009287
## 46 1.5258416 1.4457536 0.7048007
## 47 1.7325510 1.5823929 0.8628512 0.5765737
## 48 3.4799926 3.3540708 2.1320414 2.2873933 2.0495159
## 49 4.9818033 4.8226112 3.7670774 3.6979452 3.3319549 1.9552306
## 50 2.6656173 2.5508278 1.4125661 1.3929076 1.1893861 1.1537503
## 51 2.2235973 2.1127564 1.3375224 1.5282156 1.4343145 2.0238261
## 52 2.4411424 2.3936641 1.4409522 1.8096384 1.8874243 1.9917875
## 53 1.3880445 1.3930188 1.6665525 2.0604096 2.2090577 3.3963995
## 54 1.3895288 1.3445887 1.3896911 1.5640044 1.6843420 3.0425466
## 55 4.4411206 4.3766386 4.0124831 4.0775953 4.0233397 4.1959998
## 56 4.6566657 4.6640311 4.8831673 5.2431568 5.2645913 5.8273040
## 57 4.2910209 4.2914560 4.2284635 4.4736568 4.5442132 4.9763905
## 58 5.0269410 5.0424488 5.0447566 5.3347999 5.3932379 5.7665404
## 59 2.0101522 2.0025600 1.9164472 2.2061971 2.3345930 3.2716414
## 60 2.3440695 2.2991183 1.6754228 1.8590179 1.9621712 2.5416982
## 61 3.0468644 2.9752052 2.0633736 2.2034654 2.1815967 2.0447665
## 62 3.8315735 3.7606565 2.6508080 2.8574556 2.8025032 1.7630215
## 63 2.8084421 2.7910359 2.0723515 2.5216482 2.6263519 2.6183634
## 64 2.4879949 2.4291096 2.1553363 2.6599481 2.6420124 3.0608260
## 65 3.2067151 3.1861913 2.9173903 3.5324318 3.5143856 3.5854330
## 66 3.7089786 3.7181786 3.8392682 3.9624851 4.0674293 4.8885074
## 67 3.9184502 3.8855216 3.7145922 3.7216441 3.7588817 4.3453569
## 68 1.3853910 1.3490450 1.3359757 1.4034956 1.5765214 3.0091858
## 69 2.1999386 2.0991477 1.4536378 1.3253685 1.3100885 2.2931502
## 70 1.6394660 1.5901616 1.1702386 1.2955010 1.4550548 2.6340064
## 71 1.0808584 1.0611542 1.7127745 1.8841906 1.9992088 3.5667248
## 72 1.3166889 1.2459375 1.3035799 1.2607838 1.3398381 2.9580943
## 73 1.0579184 1.0839398 1.6342248 1.6460226 1.8746938 3.5415358
## 74 1.0634820 1.0351752 1.6346479 1.7225672 1.8363945 3.4783959
## 75 1.5691645 1.5522220 2.0457759 2.0616782 2.1793305 3.7367039
## 76 2.1205760 2.0751633 1.5412476 1.7278860 1.7997784 2.5713550
## 77 3.0757211 3.0149723 2.0694162 2.2568047 2.2230419 1.9696669
## 78 2.2523365 2.1918179 1.6019938 1.6663470 1.7021351 2.4761405
## 79 2.4203319 2.3345751 1.5679828 1.7778377 1.7105530 2.1063972
## 80 2.0187831 1.9730580 1.5318923 1.4500922 1.5851987 2.7008830
## 81 1.8186503 1.8247264 1.8680722 2.2867160 2.3952384 3.3407276
## 82 2.6977002 2.6738073 1.9043242 2.3541669 2.4314391 2.4284166
## 83 1.5981847 1.5847734 1.4675984 1.7394755 1.8823633 3.0066514
## 84 1.9520815 1.9322957 1.3572502 1.6232047 1.7711189 2.5599628
## 85 1.7318168 1.6575645 0.8885072 1.3250026 1.3502586 2.1716103
## 86 2.0352455 2.0247648 1.4383606 1.9114407 2.0156008 2.5527688
## 87 1.8949826 1.7825903 0.9298010 0.9773747 0.8362141 1.9320920
## 88 2.1301340 2.0951345 1.2198718 1.3565854 1.4974582 2.1427567
## 89 3.3374398 3.3242250 2.5545031 2.9619491 3.0447118 2.7556599
## 90 2.7406653 2.7325649 2.3129114 2.7514493 2.8093898 3.0945574
## 91 2.6214452 2.5818620 1.7740498 1.9848130 2.0407789 2.2653225
## 92 2.8442743 2.8133229 1.9318538 2.1479900 2.2267132 2.2301897
## 93 2.6513079 2.6180798 2.1187239 2.3044625 2.3674909 2.8613439
## 94 2.1338955 2.1359857 2.1188480 2.1690584 2.3091144 3.4529474
## 95 3.3163540 3.2663327 2.4081950 2.5505644 2.5639114 2.3688328
## 96 2.3401010 2.3545625 1.8611525 2.2233105 2.3039180 2.8074648
## 97 2.7090474 2.6456027 1.6520744 1.7810185 1.7713382 1.7969808
## 98 4.1385635 4.1416213 3.9327288 4.4665547 4.4649939 4.4717377
## 99 3.5183540 3.5438518 3.8086809 4.2707519 4.2773182 4.9271704
## 100 3.0656046 3.0539114 2.7904327 3.2767257 3.2811854 3.5281010
## 101 3.5934715 3.5610971 2.9210197 3.1840405 3.1740835 3.0472434
## 102 3.3488907 3.3268014 2.7820567 3.0522995 3.0832783 3.1648142
## 103 5.0907395 5.1379601 4.5131549 4.6573001 4.6615489 4.3922310
## 104 3.8834796 3.8183103 2.9060771 2.9586696 2.9091178 2.4275402
## 105 3.9518971 3.8984873 3.0028697 3.0658058 3.0425914 2.5803482
## 106 4.3880768 4.3144640 3.3607576 3.3258941 3.2297931 2.5580354
## 107 4.3656987 4.2750105 3.3427284 3.2880930 3.1374162 2.4853883
## 108 3.9460153 3.8810302 3.0228088 3.0454637 2.9777366 2.5917605
## 109 4.1684106 4.1108045 3.2058100 3.3523758 3.3151884 2.6718104
## 110 4.1004549 4.0214726 3.0982922 3.1653979 3.0606028 2.4229424
## 111 3.0392983 2.9634523 2.3885853 2.3931265 2.3234728 2.7156517
## 112 3.5642470 3.5154706 2.7585504 2.9938845 2.9783721 2.7173876
## 113 4.1443160 4.0654063 3.0869531 3.0621173 2.9609800 2.2902713
## 114 4.2089906 4.1200772 3.1288561 3.1591678 3.0273000 2.2176014
## 115 3.7071101 3.6626639 2.7915908 2.8562936 2.8791706 2.5734504
## 116 4.0077458 3.9452852 2.9846454 2.9690670 2.8760628 2.3058269
## 117 3.3044040 3.2444375 2.4384623 2.4921132 2.4636472 2.4139357
## 118 3.5534917 3.5132816 2.6076123 2.6338266 2.6788044 2.4308670
## 119 3.5913267 3.5324283 2.6951562 2.6394788 2.5403329 2.4027481
## 120 3.2827464 3.2148173 2.4138579 2.2725937 2.2339936 2.3877547
## 121 4.3187583 4.2642459 3.6786573 3.6227672 3.5686844 3.5951722
## 122 4.6161964 4.5645424 3.8596448 3.8541211 3.8040267 3.5378976
## 123 4.9792186 4.9087336 4.1355576 4.1246891 4.0112055 3.5209730
## 124 5.5865892 5.4798745 4.6621758 4.6024264 4.3824123 3.6722256
## 125 5.0707923 5.0025483 4.1988242 4.1671293 4.0696564 3.5381356
## 126 4.7525173 4.6987045 3.9775702 3.9727015 3.9128050 3.5859285
## 127 5.7896105 5.6804820 4.8636042 4.7482189 4.5177328 3.8323285
## 128 5.3327414 5.2665432 4.4777176 4.3937948 4.3225472 3.8380700
## 129 5.2575079 5.1906355 4.4438475 4.5088422 4.4327816 3.8818456
## 130 5.3796252 5.3041866 4.5032905 4.3995464 4.3139775 3.8044884
## 131 5.1073671 5.0578912 4.3269348 4.4230355 4.3912580 3.8967385
## 132 5.0320570 4.9862680 4.2535689 4.3327784 4.3119024 3.8518932
## 133 4.9695244 4.9376832 4.2404957 4.3538583 4.3447264 3.9376641
## 134 5.0684997 5.0144089 4.2354976 4.2118122 4.1666011 3.7073814
## 135 5.4667455 5.4314877 4.6294900 4.6025798 4.5309872 3.9810210
## 136 5.2468712 5.1724290 4.4080021 4.4613320 4.3610437 3.7751603
## 137 5.1810197 5.1157334 4.3526258 4.3230077 4.2407819 3.7685352
## 138 5.2323394 5.1691909 4.4227810 4.4909277 4.4290671 3.8892887
## 139 5.6387475 5.5463048 4.7330156 4.6559555 4.5166793 3.8781680
## 140 5.3784541 5.2988007 4.5306742 4.5306530 4.4150159 3.8430335
## 141 5.6879299 5.5769492 4.8095493 4.7730927 4.5732985 3.9238997
## 142 6.7967534 6.6685913 5.8728891 5.6672288 5.3994188 4.7063925
## 143 7.9084727 7.8245170 7.2119146 7.0962501 6.9584366 6.5092160
## 144 6.7719637 6.6771225 5.9687467 5.8486161 5.6804085 5.1359349
## 145 7.1507639 7.0510092 6.3298038 6.1208510 5.9481789 5.4341578
## 146 7.1836946 7.1204243 6.4487118 6.4417034 6.2525742 5.6507580
## 147 6.6746782 6.6693215 6.0119474 5.9724147 5.9307385 5.5367078
## 148 7.0494915 6.9507254 6.2496563 6.0515642 5.8687190 5.3843413
## 149 6.8012146 6.7114989 6.0351257 5.8839465 5.6976614 5.2374581
## 150 6.3740747 6.3059886 5.6259661 5.5307170 5.4185514 4.9832241
## 151 5.9780690 5.9402380 5.3300076 5.3535769 5.3150522 4.9713994
## 152 6.1436401 6.1257534 5.4661281 5.3881183 5.3930482 5.0869296
## 153 7.2488515 7.2387101 6.7293113 6.5934832 6.6278033 6.5231339
## 154 6.2492854 6.2313869 5.5826216 5.5543866 5.5126320 5.1492408
## 155 7.2209206 7.1901432 6.6644295 6.6752455 6.6377919 6.3289472
## 156 7.7294585 7.7394623 7.3056886 7.3279902 7.2946466 7.1148979
## 157 7.0134853 7.0276701 6.4102928 6.3303534 6.3118754 6.0180167
## 158 5.1547252 5.1860037 4.7848461 5.0656708 5.1035529 4.9934828
## 159 4.8185914 4.8330814 4.1308384 4.2033189 4.2921904 4.0194386
## 160 5.9098404 5.9065380 5.3570819 5.4692103 5.5089351 5.2340246
## 161 6.0918073 6.1118264 5.6633267 5.7475170 5.8138755 5.7173542
## 162 5.6322486 5.6769681 5.4836608 5.8361368 5.8741116 5.9102043
## 163 7.1134102 7.1415850 6.9571728 7.2791158 7.2991885 7.2374451
## 164 7.3278793 7.3426563 7.2034904 7.5699965 7.5587320 7.4798848
## 165 4.5979120 4.5660442 3.8226703 3.8288370 3.8360092 3.5387451
## 166 4.8453206 4.8687786 4.2028110 4.3019859 4.3248010 4.0631777
## 167 5.9434722 5.9703055 5.7545552 6.1528648 6.1497318 6.0591388
## 168 4.6405981 4.6546341 4.0439785 4.0718328 4.0637343 3.9734875
## 169 4.8109100 4.8047610 4.0951446 4.2146854 4.2063362 3.8274458
## 170 4.7255666 4.7047213 3.9800288 4.1064418 4.0923357 3.6835678
## 171 4.9095912 4.8815729 4.0710589 4.0712255 4.0350469 3.5584060
## 172 4.7940626 4.7683276 3.9577277 3.9674998 3.9738270 3.5284582
## 173 3.7454134 3.6864866 2.6929238 2.6062503 2.5466065 2.1072021
## 174 3.3324675 3.3007145 2.4333411 2.6270902 2.6641931 2.4195800
## 175 2.9182017 2.8895790 2.0549160 2.0119761 2.0936704 2.3479221
## 176 1.9770654 1.9986797 2.0469077 2.2531784 2.3730365 3.4623935
## 177 2.1501078 2.0981851 1.4821434 1.4804132 1.5328115 2.4265960
## 178 2.8317831 2.8306533 2.0484401 2.2703728 2.4059046 2.5413009
## 179 3.1367045 3.1283330 2.5651822 2.9198941 2.9573846 3.0264095
## 180 2.9851333 3.0071390 2.8328547 3.2016809 3.2511597 3.7324060
## 181 4.2129420 4.1991437 3.8686045 4.3406882 4.2929116 4.1838507
## 182 2.8960615 2.8924262 2.4694873 2.6170667 2.6192432 3.1182847
## 183 3.9727270 3.9905583 3.4960186 3.9060641 3.9456222 3.7986862
## 184 3.6616195 3.6758746 2.9439643 3.2554970 3.3345252 3.0807923
## 185 3.6050064 3.5582227 2.5604106 2.5404551 2.4879418 2.0559395
## 186 2.8464828 2.7888074 2.0229902 2.1855798 2.0809108 2.2178134
## 187 4.2041593 4.2298319 4.3441911 4.8019187 4.7846011 5.2036937
## 188 3.1966446 3.1951784 3.1576224 3.4077931 3.4389761 4.0850227
## 189 2.8402674 2.8682434 2.9753851 3.1854195 3.2870142 4.1787328
## 190 3.3730430 3.3785297 3.4560348 3.8157627 3.8408739 4.4462744
## 191 3.1361207 3.1634153 3.4710238 3.8336164 3.8698276 4.7128309
## 192 2.9035491 2.9228333 3.0308500 3.3682000 3.4490186 4.2046895
## 193 3.2967384 3.3321126 3.6081802 4.0132631 4.0804623 4.8373334
## 194 3.1040532 3.1159121 3.4900253 3.7478468 3.8056258 4.7978108
## 195 3.0299448 3.0573632 3.2896064 3.5322229 3.6249679 4.5429965
## 196 5.4258877 5.4529090 5.7175934 6.1097648 6.1111478 6.6298949
## 197 4.8734898 4.8816440 4.9800274 5.3132808 5.3481881 5.7908156
## 198 4.7849765 4.7736762 4.7716157 5.0774223 5.0577688 5.4083410
## 199 4.9207333 4.9157916 4.9663143 5.3048120 5.3018828 5.6689020
## 49 50 51 52 53 54
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
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## 39
## 40
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## 43
## 44
## 45
## 46
## 47
## 48
## 49
## 50 2.4443771
## 51 3.3643567 1.4121752
## 52 3.6176839 1.6413436 0.8656335
## 53 4.9890515 2.7820097 1.7358880 1.7639419
## 54 4.4414407 2.2397661 1.1848925 1.5270416 0.8706569
## 55 4.8857736 3.9479080 3.3695788 3.5064222 3.8966879 3.6359969
## 56 7.0561633 5.5149831 4.3344674 4.2573652 3.5681837 3.9337853
## 57 6.0820653 4.6104338 3.4040490 3.3481196 3.1558749 3.2200346
## 58 6.9107661 5.5042480 4.2463592 4.0937369 3.7807059 4.0106067
## 59 4.6919899 2.6179662 1.9385819 2.0017432 1.6678452 1.5853889
## 60 3.9408714 1.9844454 1.5728527 1.5859886 2.0777277 1.7749541
## 61 3.2226902 1.6949286 1.6721232 1.6608333 2.7576194 2.3489270
## 62 2.9184444 2.0503438 2.2811105 2.0217627 3.4581122 3.1712844
## 63 4.2488828 2.4482718 2.0543938 1.6108933 2.2460261 2.3168837
## 64 4.5532753 2.7482403 2.0877556 1.9983721 1.8776407 2.0656734
## 65 5.0690606 3.4189456 2.8331054 2.5232225 2.4427923 2.8087487
## 66 6.0823639 4.4267608 3.1529196 3.2017893 2.6843671 2.7432964
## 67 5.2467155 3.9162465 2.7557907 2.9308113 3.0166910 2.7425494
## 68 4.3962301 2.1732951 1.7080206 1.9731485 1.6148530 1.2602049
## 69 3.4398805 1.4697930 1.4052361 1.8240590 2.3296074 1.7363888
## 70 4.0691054 1.8570747 1.4807306 1.6696224 1.7165382 1.3437941
## 71 5.0608953 2.8965251 2.6097453 2.7994994 1.9161771 2.0092872
## 72 4.3121188 2.1838177 2.1591563 2.4568709 2.1307706 1.8613862
## 73 4.9989328 2.7631125 2.5500404 2.7447261 2.0020699 1.9330284
## 74 4.9131653 2.7547703 2.5173702 2.7620658 1.9799871 1.9486213
## 75 5.1517538 3.0876631 2.8819320 3.0761084 2.3403174 2.3521410
## 76 4.1341662 2.2099850 2.3254121 2.2892387 2.4507362 2.3853895
## 77 3.4867797 2.0932241 2.5710738 2.3791136 3.1946341 3.0700945
## 78 3.9484035 2.1079351 2.3446425 2.3680895 2.6400515 2.4824983
## 79 3.5925500 1.8429248 2.1349646 2.1413771 2.6325251 2.4632770
## 80 4.0967564 2.1049036 2.2891540 2.3968154 2.5331545 2.2780611
## 81 5.0027539 2.9207886 2.2538736 2.1091376 1.4086513 1.8149719
## 82 4.1778398 2.3955748 2.0495590 1.5510512 2.1837297 2.3307848
## 83 4.5839632 2.4401084 1.8022391 1.7947265 1.3691064 1.4157173
## 84 4.1662566 2.0751355 1.5782275 1.4393896 1.6764544 1.5745710
## 85 3.8933315 1.7846703 1.8115227 1.7278142 1.9333787 1.9090013
## 86 4.3592242 2.3358662 2.3003920 1.9883216 2.0950114 2.2965265
## 87 3.4236553 1.3670691 1.6934263 1.8615389 2.2777604 1.9662641
## 88 3.8319617 1.8158177 2.0905553 1.9236380 2.4090836 2.2864461
## 89 4.5501495 3.0413624 3.1142177 2.5894357 3.1429735 3.3967120
## 90 4.8597258 3.1090340 3.0070274 2.6367627 2.6546150 3.0069563
## 91 3.9564800 2.2437251 2.4464501 2.1854762 2.7217750 2.7220888
## 92 3.9404246 2.3009586 2.5539453 2.2127582 2.8871833 2.8912541
## 93 4.3993949 2.6832399 2.4305200 2.2631787 2.5003832 2.5311458
## 94 4.9129557 2.9547381 2.5563455 2.5736356 2.2293738 2.2324550
## 95 3.7996246 2.4702886 2.5225053 2.2558526 3.1102829 3.0037250
## 96 4.5234206 2.6477048 2.6269978 2.3373999 2.4370117 2.6202263
## 97 3.4247124 1.7788639 2.1869272 1.9997381 2.8192294 2.6573051
## 98 6.1207301 4.6624821 4.4657289 4.0319259 3.8496507 4.4073537
## 99 6.5302910 4.7821259 4.4409204 4.2068368 3.4468365 4.0335776
## 100 5.2307106 3.5808893 3.4174163 3.0659729 2.9139158 3.3609910
## 101 4.4999318 3.2149892 3.6265548 3.3397879 3.7847293 3.8819752
## 102 4.7005986 3.2438994 3.5635146 3.2842777 3.5750946 3.7180589
## 103 5.3471265 4.5997188 4.9780333 4.7934155 5.3494616 5.3106253
## 104 3.5844357 2.7073421 3.4393984 3.2644203 4.1343854 3.9749176
## 105 3.7704120 2.8617407 3.5668622 3.3506075 4.1982861 4.0694230
## 106 3.3422712 2.9054011 3.7770754 3.6519817 4.6570678 4.4075952
## 107 3.1373714 2.8226308 3.7174401 3.6680812 4.6559471 4.3724553
## 108 3.6752453 2.8482890 3.5764068 3.4349496 4.2441131 4.0818513
## 109 3.9134006 3.1036205 3.7417996 3.4645659 4.3221513 4.2713365
## 110 3.4634392 2.8168390 3.5689992 3.4163945 4.3240950 4.1636602
## 111 3.9525384 2.5962459 3.1163848 3.1351015 3.5151344 3.3695208
## 112 4.2058877 2.9863836 3.2506989 2.9509852 3.5633274 3.6259342
## 113 3.1922013 2.6457322 3.3276644 3.2006808 4.2574456 4.0002286
## 114 3.1338057 2.6815021 3.3373279 3.1985732 4.2710721 4.0466872
## 115 3.9199462 2.8122136 3.2459311 2.9953602 3.8059503 3.7117098
## 116 3.2623898 2.6145910 3.2553566 3.1438558 4.1544317 3.8995776
## 117 3.7428361 2.4854526 2.9045074 2.7627076 3.4643440 3.3235031
## 118 3.7626724 2.5574414 3.0434740 2.8066914 3.6731766 3.5136502
## 119 3.4099811 2.4747805 3.0467353 3.0264301 3.8399381 3.5658378
## 120 3.4766612 2.2648616 2.8127380 2.8255060 3.5711951 3.2576480
## 121 4.4023628 3.5850527 4.1975903 4.1806003 4.7263500 4.5266922
## 122 4.3512812 3.6952959 4.3400715 4.2420002 4.9331709 4.7649096
## 123 4.0965330 3.7897996 4.5164489 4.4466071 5.2619128 5.0512660
## 124 3.7187795 4.0644416 4.8735554 4.9242383 5.8590951 5.5578847
## 125 4.0869405 3.8214682 4.5694380 4.4894433 5.3508668 5.1250022
## 126 4.3515000 3.7726507 4.4426736 4.3343124 5.0573884 4.8866769
## 127 3.6763730 4.1899952 5.0354017 5.1362097 6.0977321 5.7402436
## 128 4.2998175 4.0821817 4.8872775 4.8227969 5.6797680 5.4274080
## 129 4.6452548 4.2586458 4.9173304 4.7603958 5.5032750 5.4134257
## 130 4.1784522 4.0543010 4.8749841 4.8425667 5.7261676 5.4457964
## 131 4.8077331 4.2293733 4.8462340 4.6349704 5.3380143 5.2876893
## 132 4.7565914 4.1412390 4.7755659 4.5691646 5.2795951 5.2079922
## 133 4.9118921 4.1915503 4.7953032 4.5585162 5.2139213 5.1767640
## 134 4.3504761 3.9218954 4.6814803 4.5665659 5.3851877 5.1784053
## 135 4.4391324 4.2563313 5.0137849 4.9345224 5.8030312 5.5647020
## 136 4.4468416 4.1496159 4.8425245 4.7182268 5.4975712 5.3715187
## 137 4.3423662 4.0362722 4.7899016 4.7116079 5.5109542 5.3073752
## 138 4.6941124 4.2642921 4.9076699 4.7391569 5.4747236 5.3948710
## 139 4.1323463 4.2453720 5.0596764 5.0480809 5.9526380 5.6877173
## 140 4.3749471 4.2011353 4.9443451 4.8608209 5.6680832 5.4934731
## 141 4.1309170 4.3490454 5.1144178 5.1457545 5.9854023 5.7514523
## 142 3.9879607 5.0085433 5.9538145 6.1493648 7.1630970 6.7013276
## 143 6.3746998 6.7294090 7.1743883 7.2406139 8.0110096 7.7118225
## 144 5.0105768 5.4039933 5.9337514 6.0016909 6.8823252 6.5521101
## 145 5.0323877 5.6392326 6.2367018 6.3776239 7.3188636 6.8890111
## 146 5.6419782 6.0320796 6.4424504 6.4863284 7.2753419 7.0449574
## 147 5.8833780 5.7419093 6.1297314 6.0544502 6.8055993 6.5893296
## 148 4.9925370 5.5678411 6.1596707 6.3070682 7.2219594 6.7952213
## 149 4.9842145 5.4282470 5.9800558 6.1038430 6.9644400 6.5828641
## 150 5.1365075 5.2066884 5.6679883 5.6816882 6.4904360 6.2102952
## 151 5.5946737 5.1820334 5.5079520 5.3663204 6.0160924 5.9045205
## 152 5.5570652 5.1969904 5.6193451 5.5005175 6.2593759 6.0319915
## 153 6.8680354 6.5155892 6.8556067 6.8074980 7.4090165 7.1605619
## 154 5.5874332 5.3319419 5.7208938 5.6262680 6.3574101 6.1594827
## 155 6.7836423 6.5237417 6.7868167 6.6932115 7.2613788 7.1496064
## 156 7.5617490 7.2585657 7.4522823 7.4006825 7.8447740 7.7425632
## 157 6.2917772 6.1410355 6.5158233 6.4773768 7.1966939 6.9374786
## 158 6.2541730 5.1171377 5.1826885 4.7887550 5.0372329 5.2605912
## 159 5.1281266 4.1693977 4.4502109 4.1122962 4.8113850 4.7701628
## 160 6.1770924 5.4355356 5.6377500 5.3657957 5.8798979 5.9113934
## 161 6.6387874 5.7905259 5.9362561 5.6878883 6.0897125 6.1069361
## 162 7.2422571 5.9867053 5.9202402 5.5192523 5.4708995 5.8355021
## 163 8.3908816 7.3664226 7.3022787 6.9466897 6.9300592 7.2642642
## 164 8.6532170 7.6611215 7.5396731 7.1996329 7.1034264 7.4982410
## 165 4.4375918 3.6569902 4.0172752 3.8212879 4.6154703 4.4462467
## 166 5.0425976 4.2072096 4.4652009 4.2198277 4.8789445 4.8058547
## 167 7.3685059 6.2369228 6.1542378 5.7523998 5.7225872 6.1267767
## 168 4.8288161 4.0095517 4.2753724 4.1559798 4.7629029 4.6031433
## 169 4.8308177 4.0730051 4.3427380 4.0872643 4.7936196 4.7451894
## 170 4.7183355 3.9571361 4.2145837 3.9589235 4.6786742 4.6386740
## 171 4.2812760 3.8016663 4.1955427 4.0534867 4.9481429 4.7378153
## 172 4.3850353 3.7420854 4.1255367 3.9165498 4.8019978 4.6250656
## 173 3.0887117 2.2039437 2.8570595 2.7231777 3.8304849 3.4919461
## 174 3.9881418 2.6185915 2.8490437 2.4782080 3.2568765 3.2561734
## 175 3.7661385 2.1807727 2.4999267 2.3242650 3.0558934 2.8418290
## 176 5.0642996 3.0571236 2.7776637 2.6815007 2.1991087 2.4120648
## 177 3.9042519 1.9975514 2.0324139 2.0459021 2.3669634 2.1576709
## 178 4.2199761 2.4867102 2.5743635 2.1745685 2.7696252 2.8003582
## 179 4.6790646 3.1110984 3.0866681 2.6920408 2.9936992 3.2230438
## 180 5.3511277 3.6117208 3.5225131 3.2124894 3.0106300 3.3555337
## 181 5.7057763 4.4224878 4.3680845 3.9710291 4.0026723 4.4290801
## 182 4.4817254 2.8584284 3.0776192 2.9063419 3.1237629 3.1033232
## 183 5.3757100 3.9760667 4.0398028 3.5495545 3.8116586 4.1371764
## 184 4.6541774 3.2344509 3.4730741 2.9658832 3.5704032 3.7137314
## 185 3.1395019 2.1026566 2.8418224 2.6600202 3.7358077 3.4286157
## 186 3.6067606 2.1152369 2.5005717 2.3745837 2.9907591 2.8503115
## 187 6.7077699 5.1393723 4.9048375 4.6171647 4.0907404 4.6107778
## 188 5.4949762 3.8436585 2.9505311 2.8019261 2.4300058 2.7023894
## 189 5.6142672 3.7742732 2.7463237 2.6559070 2.0244005 2.2834739
## 190 5.9205918 4.2376398 3.2856875 3.0873487 2.4871667 2.9482677
## 191 6.1185148 4.2974463 3.2020093 3.1304916 2.1753862 2.6231115
## 192 5.6547218 3.8075234 2.6420474 2.5129356 1.7852925 2.1662834
## 193 6.3319192 4.4871960 3.3989834 3.2272988 2.2766493 2.8376896
## 194 6.1544305 4.3290752 3.0897624 3.1304530 2.0863479 2.4457421
## 195 5.9156085 4.0781799 2.8335155 2.8183247 1.9673592 2.2560720
## 196 7.9381406 6.4414858 5.4020406 5.2082774 4.4659926 4.9760270
## 197 7.0361593 5.5761622 4.3142406 4.1616241 3.6413097 4.0102804
## 198 6.5157391 5.2296684 3.9662093 3.8979038 3.5739759 3.8141041
## 199 6.8446490 5.4864115 4.2514491 4.1206728 3.6964057 4.0239051
## 55 56 57 58 59 60
## 2
## 3
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## 55
## 56 3.8841901
## 57 2.7962673 1.9240733
## 58 4.1092199 1.7108839 1.7009091
## 59 2.9665131 3.7061104 3.0892422 4.1898919
## 60 2.7143038 4.1940470 3.3429792 4.4481588 0.9780989
## 61 2.6927074 4.6302941 3.6428673 4.7452081 1.7790662 0.9262595
## 62 3.0943328 5.1083488 4.1388946 5.1000588 2.6956024 1.8519933
## 63 3.0479881 3.9699009 3.3422332 4.2562752 1.4744351 1.1503706
## 64 3.0615529 3.4779908 3.1412448 4.0749531 1.0979857 1.4230832
## 65 4.1291930 3.4643352 3.4320642 4.0491992 2.4216206 2.7543393
## 66 3.1383641 2.4416136 1.5947571 1.9887988 3.0919164 3.3006421
## 67 2.6293992 3.2317161 1.8843462 2.5981808 3.1506840 3.0558737
## 68 3.2973468 4.4161976 3.6743562 4.7278046 1.2629216 1.3816631
## 69 3.0689450 4.9359411 3.9340774 5.0741652 1.7846653 1.2974317
## 70 3.1680911 4.4811438 3.6598898 4.7246800 1.2731080 1.1193495
## 71 4.2791112 4.8309347 4.5614367 5.3520334 2.1176894 2.4091198
## 72 3.9697451 5.1204725 4.5780568 5.4855207 2.0365239 2.0168677
## 73 4.2337657 5.0048276 4.5748914 5.4332099 2.0744838 2.2880588
## 74 4.2107730 4.9307234 4.5781579 5.4116935 2.0960229 2.3329986
## 75 4.4385015 5.2259248 4.8879036 5.6025554 2.6083371 2.7530507
## 76 4.0497379 5.3112705 4.7603291 5.5085043 2.4862047 2.2086102
## 77 4.1687440 5.7576686 5.1169781 5.8121797 3.1164273 2.5484103
## 78 4.0562139 5.4891699 4.8918872 5.6476447 2.6452018 2.2766815
## 79 3.8976104 5.3810707 4.7562526 5.5472123 2.5303598 2.1267802
## 80 4.0143162 5.4904964 4.8121220 5.6450955 2.4734322 2.1684512
## 81 3.4769443 3.5056991 3.3640545 4.0126352 1.6461674 1.8896984
## 82 3.2894956 4.0455130 3.5523550 4.2369131 2.0720451 1.6873481
## 83 3.1619785 3.7771192 3.3142647 4.1417577 1.3338655 1.3826382
## 84 3.0090745 4.0071614 3.3596692 4.2283191 1.4435885 1.0992805
## 85 4.0525008 4.8225652 4.3635338 5.0829184 2.1557203 1.8825691
## 86 4.3314358 4.7685889 4.4679175 5.0436659 2.4366481 2.2521206
## 87 3.9738649 5.1511330 4.5506444 5.3401255 2.3457567 1.9078021
## 88 4.2016532 5.2324097 4.6645337 5.3578830 2.5696553 2.1013886
## 89 4.9350665 5.3867263 5.0548139 5.4369195 3.5461220 3.1768029
## 90 4.8907735 4.9772079 4.8633508 5.1956265 3.2433589 3.0951849
## 91 4.5212404 5.3792948 4.8786502 5.4181717 3.0885575 2.6334363
## 92 4.5780583 5.4791865 4.9439864 5.4754441 3.2102223 2.7089073
## 93 3.8473175 4.6760315 4.2736668 4.7379102 2.7676428 2.4405394
## 94 3.9522288 4.5576252 4.2219941 4.7151612 2.5976469 2.5148713
## 95 3.8631564 5.1449403 4.5501827 5.0467653 3.1770760 2.5872264
## 96 4.5733274 4.9625026 4.6932760 5.1548659 2.9151185 2.7154070
## 97 4.2671141 5.4597230 4.8188844 5.4721304 3.0098502 2.4276627
## 98 5.8838689 5.1560084 5.5772462 5.5750052 4.4464616 4.4904110
## 99 5.8857600 4.8168452 5.4338548 5.4342744 4.1835184 4.4678335
## 100 5.1003205 4.8604574 4.9858338 5.2135624 3.5222509 3.4887194
## 101 4.5648237 5.8058569 5.5561262 6.1512492 3.5358995 3.1286500
## 102 4.5274249 5.6717145 5.4419936 6.0548803 3.3540800 3.0130621
## 103 5.6770244 7.1513100 6.6913872 7.3104779 5.0316249 4.6515319
## 104 4.3527671 6.3537282 5.7436343 6.5192559 3.7003416 3.0004168
## 105 4.4696198 6.3905408 5.8123003 6.5486105 3.8009585 3.1183265
## 106 4.6080033 6.8061542 6.1389818 6.8945037 4.2151513 3.4493315
## 107 4.5458894 6.8058990 6.1394055 6.9153632 4.2015002 3.4386351
## 108 4.4764543 6.4471818 5.8833464 6.6180988 3.8604738 3.1803430
## 109 4.6161930 6.4051012 5.8925417 6.5765256 3.9752797 3.3178763
## 110 4.4491076 6.4691073 5.8858638 6.6341932 3.9116114 3.2047003
## 111 4.1302886 5.9054159 5.4273756 6.2342990 3.1321463 2.6359045
## 112 4.8273894 5.9389811 5.4891420 5.9197454 3.7685793 3.2983795
## 113 4.8156209 6.6667226 5.9100909 6.4861033 4.2213767 3.4982053
## 114 4.8170295 6.6255084 5.9008699 6.4632101 4.2434471 3.5289207
## 115 4.8084992 6.3127695 5.6567065 6.1838532 3.9041258 3.2914524
## 116 4.7693676 6.5994875 5.8422040 6.4301215 4.1176813 3.4228424
## 117 4.5729301 6.0488614 5.4209920 5.9807303 3.5616521 3.0017194
## 118 4.6575457 6.2424074 5.5159652 6.0965051 3.7095777 3.0791780
## 119 4.6418258 6.3796292 5.6702326 6.2671333 3.8418263 3.2236068
## 120 4.4901816 6.2575354 5.4865641 6.1469566 3.5688976 2.9501512
## 121 5.7135843 7.1003771 6.6522584 7.1568380 4.7440755 4.2849147
## 122 5.8158171 7.2421083 6.7707870 7.2551733 4.9352047 4.4190773
## 123 5.9300612 7.4848301 6.9927021 7.4730652 5.2245358 4.6544722
## 124 6.1681277 8.0008490 7.4377238 7.9621697 5.7582898 5.1215122
## 125 5.9676282 7.5951529 7.0550322 7.5533599 5.2962789 4.6972746
## 126 5.8936743 7.3245572 6.8653589 7.3275633 5.0592837 4.5289150
## 127 6.2849706 8.2571441 7.6323215 8.1903401 5.9638875 5.3028257
## 128 5.5442881 7.8405552 7.1661140 7.8853857 5.2664543 4.6129226
## 129 5.6006277 7.5361303 7.0484391 7.6661570 5.1941114 4.6231521
## 130 5.5197454 7.9057676 7.1875722 7.9418280 5.2895845 4.6184594
## 131 5.5481480 7.3698044 6.9017241 7.5097982 5.0304486 4.4952553
## 132 5.4826640 7.3388090 6.8436982 7.4710993 4.9480052 4.4100108
## 133 5.5114161 7.2196139 6.7932805 7.3771097 4.9014901 4.4116663
## 134 5.3678622 7.5279624 6.8927737 7.6069910 4.9587374 4.3523310
## 135 5.6478256 7.8956029 7.2187605 7.9369223 5.3589763 4.7499633
## 136 5.5193001 7.5345676 7.0172396 7.6626691 5.1530785 4.5691638
## 137 5.4668464 7.6413707 7.0362119 7.7309525 5.1216690 4.5091263
## 138 5.5945350 7.5223759 7.0258675 7.6497272 5.1671972 4.5986482
## 139 5.6786441 8.0650162 7.3864378 8.1112581 5.5488104 4.8676642
## 140 5.6053146 7.7266707 7.1765789 7.8288362 5.3187540 4.7030710
## 141 5.7270819 8.0264942 7.4361025 8.1296353 5.6228311 4.9791380
## 142 6.4196968 9.1427785 8.3628598 9.1262963 6.6877460 5.9663178
## 143 8.4360126 9.9694999 9.2445818 9.5613233 8.1308896 7.6086777
## 144 7.4140030 9.0422697 8.2833307 8.6083631 7.0333692 6.4476957
## 145 7.6342558 9.5235254 8.6364498 9.0496045 7.3876649 6.7569891
## 146 7.8373532 9.2604216 8.6297404 8.8871373 7.4513947 6.9470921
## 147 7.6120248 8.9392329 8.2292267 8.4884884 6.9913516 6.5121342
## 148 7.5735680 9.4042890 8.5533863 8.9472105 7.2996426 6.6899542
## 149 7.4422161 9.1180121 8.3477105 8.6907055 7.0835532 6.5141763
## 150 7.2244663 8.7175405 7.9748814 8.2827113 6.6864209 6.1409764
## 151 7.1433158 8.1718095 7.6114984 7.7798111 6.3402237 5.8969810
## 152 7.2151612 8.5072449 7.7768819 8.0317152 6.4811454 5.9807951
## 153 8.2093758 9.5028100 8.7409456 9.0494885 7.5681734 7.1397821
## 154 7.2933576 8.5294793 7.8643064 8.0936248 6.5898818 6.1164758
## 155 8.1612357 9.1812811 8.6213875 8.8165019 7.5093053 7.1184298
## 156 8.7299246 9.6623438 9.1457631 9.3362640 8.0689972 7.7624840
## 157 7.9184621 9.3200286 8.5434167 8.8544381 7.3253554 6.8691119
## 158 6.8899062 6.8418367 6.8142223 6.6185431 5.6924662 5.5163143
## 159 6.3045731 7.1775552 6.6054022 6.7348904 5.2979772 4.8487647
## 160 7.2757463 7.9560483 7.5099703 7.5864096 6.2855209 5.9290393
## 161 7.4410631 8.0123503 7.6110186 7.6757171 6.5232907 6.2333695
## 162 7.4932613 6.8905686 7.1786989 6.8154882 6.1972733 6.1855349
## 163 8.6285875 8.0356917 8.3330831 7.9858670 7.5360714 7.5216558
## 164 8.8356451 8.0760768 8.4953992 8.1054621 7.7472908 7.7733450
## 165 5.9655446 7.0891942 6.4151867 6.6546670 5.0445086 4.5449472
## 166 6.2991835 7.1763721 6.6287596 6.7760008 5.3221757 4.9240507
## 167 7.6787715 6.9959143 7.3663088 6.9647229 6.4498386 6.4384980
## 168 6.1515732 7.1618414 6.5579864 6.7783752 5.1849914 4.7945063
## 169 6.2115733 7.1066214 6.5784790 6.7157399 5.2726974 4.8363730
## 170 6.1179402 7.0293480 6.4865349 6.6423289 5.1725772 4.7247284
## 171 6.0685131 7.3956823 6.6443635 6.9406955 5.2975641 4.7535960
## 172 6.0319889 7.2687202 6.5364140 6.8043780 5.1870630 4.6469446
## 173 4.9058632 6.3117706 5.5438220 6.0308637 4.0053239 3.3120096
## 174 4.9595189 5.7435567 5.2275007 5.5740644 3.6965217 3.1819939
## 175 4.7509358 5.7987373 5.1243092 5.6027744 3.4320027 2.8861229
## 176 4.9675071 5.0023337 4.8056952 5.1187597 3.0603373 3.0511453
## 177 4.5162627 5.3468192 4.7413725 5.2781469 2.8863841 2.5199062
## 178 4.8103299 5.4322415 4.9065055 5.2939495 3.2718394 2.8586316
## 179 5.1342160 5.3120542 5.1055805 5.2981615 3.6239402 3.3596671
## 180 5.3654435 5.0187172 5.1692118 5.3167847 3.6375506 3.6040235
## 181 5.9594798 5.4064044 5.7647125 5.7289433 4.5640090 4.4844801
## 182 5.0378209 5.3755684 5.1958360 5.5093223 3.5212551 3.2646267
## 183 5.7136735 5.4765948 5.5836728 5.6414373 4.2849163 4.0952748
## 184 5.2924681 5.5852805 5.3621483 5.6036029 3.9115173 3.5405596
## 185 4.8140713 6.0675212 5.4151598 5.9465160 3.7912024 3.1286349
## 186 4.6539148 5.3993857 5.0097136 5.4730439 3.2630767 2.8249833
## 187 6.3960386 5.1816471 5.8919524 5.7303985 4.7581202 4.9693840
## 188 4.1448757 3.6133120 3.4706405 3.3482693 3.3563593 3.3783787
## 189 3.9878028 3.4333847 3.1234609 3.1564604 3.0073245 3.1413415
## 190 4.3986426 3.2771875 3.4393348 3.1709331 3.4696921 3.6498436
## 191 4.2945340 2.8055107 2.9779295 2.8421696 3.1312168 3.5597812
## 192 3.8673508 2.9213869 2.6138329 2.7099685 2.7453862 3.0407590
## 193 4.4600218 2.7825782 3.0493132 2.8289257 3.2599075 3.6894050
## 194 3.9749643 2.3031388 2.3755725 2.3407041 3.0823585 3.4821445
## 195 3.7659278 2.4219980 2.1747819 2.2505811 2.9122208 3.2307934
## 196 5.8856111 2.9127694 4.1348736 2.9795694 5.3091842 5.6896870
## 197 5.0196778 2.7127365 2.8580678 1.7747893 4.6245868 4.9041565
## 198 4.6867623 2.8666238 2.7182563 1.8513837 4.4853178 4.6788140
## 199 4.9524572 2.7421993 2.8933920 1.8137432 4.6447589 4.8909172
## 61 62 63 64 65 66
## 2
## 3
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## 58
## 59
## 60
## 61
## 62 1.1078029
## 63 1.4114758 1.7359429
## 64 1.9044459 2.4932439 1.1459087
## 65 2.9836576 3.2980285 2.1228333 1.7218952
## 66 3.7765719 4.3522871 3.5109380 3.3336373 3.9394693
## 67 3.2777992 3.7981184 3.4573468 3.4421948 4.1837472 1.2421256
## 68 2.0611265 2.9603350 2.1164640 1.9399647 3.0196374 3.2917746
## 69 1.4843197 2.3187867 2.1981212 2.2757262 3.3846478 3.6722436
## 70 1.7063418 2.5537814 1.8276214 1.8242920 2.9068173 3.3548400
## 71 3.1102076 3.8276051 2.8069469 2.4486976 3.4298892 3.9674754
## 72 2.5549297 3.2901191 2.6487020 2.4878574 3.5770501 4.0346992
## 73 2.9900165 3.7625149 2.8233256 2.6122671 3.6375155 3.9615512
## 74 3.0092566 3.7546786 2.8348952 2.5108059 3.5385473 3.9778690
## 75 3.3911070 4.0614578 3.1848584 2.9594988 4.0194150 4.1099603
## 76 2.5512843 2.9209781 2.3937294 2.5663014 3.5869811 4.2114400
## 77 2.5028225 2.4297668 2.5038108 2.9773319 3.8262256 4.7071031
## 78 2.5503671 2.9051012 2.5549729 2.7660346 3.8109473 4.3068202
## 79 2.2587093 2.5492779 2.3054619 2.4988970 3.4917884 4.3365353
## 80 2.5264835 3.0549241 2.6376417 2.8046460 3.9093622 4.2039213
## 81 2.5837957 3.1485476 1.7873759 1.5664077 2.3337740 2.9744058
## 82 1.9276598 2.0380606 1.1064372 1.7178415 2.3406251 3.4267906
## 83 2.1143129 2.8120623 1.6882648 1.6163122 2.6331771 2.8751721
## 84 1.6748264 2.2766471 1.3697775 1.6543541 2.6564338 3.0255716
## 85 2.2420044 2.6422864 1.9736764 2.1163857 2.7512781 3.9904899
## 86 2.6314770 2.8898369 2.0157388 2.2624989 2.6549350 4.1047404
## 87 2.1204987 2.5826279 2.3221675 2.4741874 3.2394382 4.1244174
## 88 2.3570839 2.6278691 2.2382622 2.6569652 3.3158983 4.2000010
## 89 3.3184037 3.1167534 2.6312197 3.1669807 3.3148107 4.7414985
## 90 3.4271090 3.5050422 2.6777581 2.8985429 3.0418803 4.4392259
## 91 2.8087354 2.8644293 2.5513400 2.9867167 3.4750949 4.3964311
## 92 2.8268266 2.7893471 2.5514728 3.0859223 3.5295943 4.5027442
## 93 2.7496249 2.9800484 2.4431755 2.7268317 3.6865820 3.6266835
## 94 3.0471481 3.5706931 2.7923655 2.8464343 3.8825082 3.3891419
## 95 2.5690394 2.4894992 2.5046666 3.0569563 3.9252221 4.0707843
## 96 3.0447463 3.2218595 2.5125160 2.7671949 3.0324180 4.2271538
## 97 2.4534166 2.4888381 2.4693629 2.9506785 3.4662758 4.4075432
## 98 4.7841505 4.7299306 3.7670408 3.8028307 3.3457697 5.3386331
## 99 4.9577359 5.2267506 4.0223168 3.7525159 3.4270818 5.0178482
## 100 3.8247461 3.8966210 2.9716783 3.0379131 2.9270706 4.6181463
## 101 3.2197961 3.1125124 2.7894146 3.2210014 3.9004829 5.2587424
## 102 3.2169545 3.2020463 2.6986263 3.0838150 3.8300957 5.1007879
## 103 4.6045830 4.2981222 4.5504804 4.9411964 5.5752075 6.4352157
## 104 2.8268179 2.5680262 2.9621572 3.5621974 4.4559960 5.4550123
## 105 2.9726384 2.6982741 3.0294661 3.6582297 4.5112025 5.5057246
## 106 3.1372519 2.7954710 3.4875798 4.1073096 4.9527251 5.8478658
## 107 3.1043337 2.8048744 3.5456096 4.0900130 4.9669701 5.8477037
## 108 3.0331084 2.8044137 3.1775087 3.7342471 4.6228974 5.5361966
## 109 3.1645149 2.7726261 3.0734185 3.7054972 4.4758450 5.6295121
## 110 2.9737993 2.6377681 3.1415880 3.7047705 4.5611951 5.6137638
## 111 2.7700111 2.9449463 2.8482647 3.1289482 4.2074306 4.9877417
## 112 3.3417042 3.1669201 3.0304291 3.4874517 4.1499994 4.9933761
## 113 3.2254949 2.9322166 3.5429492 4.1157333 4.8921746 5.4508341
## 114 3.2360226 2.8851054 3.5101316 4.0601906 4.8053070 5.4812667
## 115 3.2505054 3.0455584 3.2154369 3.8005149 4.5933805 5.1133681
## 116 3.1845851 2.9070830 3.4950531 4.0401544 4.8442490 5.3666480
## 117 2.9994097 2.9627622 3.0360855 3.4910457 4.3293284 4.8654768
## 118 3.0149860 2.8788830 3.0735298 3.6805277 4.4918464 4.9997797
## 119 3.0983205 3.0212062 3.4098782 3.8432567 4.7089950 5.1163725
## 120 2.9012478 2.9837580 3.2419787 3.6778817 4.6289442 4.8926719
## 121 4.2389904 4.2486790 4.4283507 4.7581883 5.6187780 6.1214895
## 122 4.3045848 4.1640658 4.4547540 4.8719576 5.6779088 6.2961999
## 123 4.4346127 4.2094925 4.6877542 5.1076782 5.8758426 6.5660508
## 124 4.7697218 4.4696531 5.2439209 5.6071406 6.4001829 7.0531453
## 125 4.4602895 4.2099311 4.7414407 5.2012785 5.9861309 6.6281037
## 126 4.3889372 4.2224754 4.5447571 4.9773059 5.7504833 6.3981303
## 127 4.9218799 4.6362485 5.5032826 5.8657988 6.6955742 7.2347385
## 128 4.3586697 4.1047308 4.7153715 5.2289968 6.2490537 6.7935675
## 129 4.4529571 4.1285160 4.5069206 4.9746549 5.9047120 6.6996967
## 130 4.3390671 4.0857680 4.7620455 5.2641171 6.3143929 6.8263321
## 131 4.3694871 4.0673177 4.3239228 4.8189887 5.7220217 6.5668234
## 132 4.2815707 4.0078704 4.2666531 4.7727471 5.6879463 6.5111564
## 133 4.3137093 4.0649142 4.2169007 4.7104778 5.5626258 6.4689297
## 134 4.1322751 3.9001185 4.3836925 4.8972667 5.8834172 6.5644801
## 135 4.4780245 4.1484170 4.8198039 5.3105589 6.2818327 6.9049482
## 136 4.3598638 4.0404653 4.4900610 4.9394298 5.8801806 6.6933392
## 137 4.2894358 4.0326320 4.5561495 5.0289474 6.0335762 6.6721472
## 138 4.4426732 4.1155782 4.4755033 4.9542628 5.8949031 6.6739892
## 139 4.5550756 4.2287889 4.9780933 5.4410807 6.4689565 7.0339769
## 140 4.4662795 4.1576286 4.6942142 5.1469224 6.1096135 6.8207153
## 141 4.6785426 4.3501668 5.0676126 5.4306101 6.4451566 7.0852715
## 142 5.4745065 5.2085860 6.2950253 6.6471902 7.6280120 8.0591208
## 143 7.3291668 7.1290477 7.7739916 8.0899235 8.7551240 8.8034969
## 144 6.1271555 5.8962860 6.6174049 6.9705177 7.6952073 7.7991651
## 145 6.3869436 6.1874207 7.0514031 7.4194408 8.2136194 8.1504214
## 146 6.6621423 6.3172122 7.0217795 7.2924169 7.9482290 8.1824755
## 147 6.3161991 6.0462532 6.5813861 6.9906225 7.6503246 7.7262505
## 148 6.3257685 6.1478794 6.9797525 7.3234456 8.0942765 8.0708602
## 149 6.1815871 6.0019006 6.7537800 7.0693205 7.8002864 7.8608717
## 150 5.8950572 5.6819649 6.2793071 6.6524011 7.3873680 7.4527271
## 151 5.7754493 5.5776337 5.8427529 6.2313550 6.8343779 7.0816126
## 152 5.8100828 5.6363377 6.0474715 6.5218385 7.1838692 7.2405660
## 153 7.0235148 6.9510340 7.3069299 7.7139903 8.3873052 8.2164395
## 154 5.9388430 5.7136870 6.1555443 6.5640673 7.2054826 7.3470688
## 155 7.0020561 6.8073213 7.1025991 7.4280708 7.9940051 8.1581653
## 156 7.6913125 7.5051737 7.7945434 8.0411800 8.6045195 8.6732987
## 157 6.6822143 6.4519817 7.0172012 7.4153509 8.1030541 8.0449903
## 158 5.6102016 5.4980034 5.0841139 5.3999806 5.4769791 6.2401406
## 159 4.8099776 4.6120523 4.6812366 5.2379655 5.7241363 5.9482486
## 160 5.9116352 5.7104772 5.7235904 6.1395126 6.6419033 6.9868235
## 161 6.2580203 6.1485055 6.0816577 6.4597659 6.8197197 7.0354233
## 162 6.3758477 6.3342426 5.6591335 5.8275406 5.6969806 6.6467351
## 163 7.6690548 7.5866488 7.0209633 7.1593515 6.9998981 7.9137264
## 164 7.9416647 7.8442761 7.2290944 7.2837742 7.0842471 8.0982518
## 165 4.4279738 4.2921416 4.5232406 5.0065857 5.5923723 5.7797873
## 166 4.8587245 4.6578491 4.8120476 5.2511031 5.7310822 6.0136539
## 167 6.6031037 6.4956260 5.8461783 5.9714246 5.7786593 6.8912658
## 168 4.7364259 4.6319302 4.8349861 5.1959048 5.7800671 5.8953694
## 169 4.7531216 4.5084875 4.6792931 5.1239470 5.6152720 5.9607819
## 170 4.6429580 4.3971559 4.5595409 5.0020543 5.5174912 5.8716241
## 171 4.5653494 4.3067652 4.7756886 5.2511092 5.8939176 6.0422061
## 172 4.4886237 4.2560863 4.6172876 5.1404712 5.7505875 5.9253930
## 173 3.0633852 2.9317644 3.4349866 4.0169663 4.4997046 5.0789384
## 174 3.2033290 3.0538944 2.9640611 3.5168784 3.8786904 4.7261399
## 175 2.9432443 3.0330520 3.0161996 3.5218810 4.0826286 4.5193631
## 176 3.5522620 3.9617040 3.0919387 3.1133167 3.5606187 4.0519499
## 177 2.7681734 3.1144715 2.7904584 3.0311196 3.6793854 4.0944396
## 178 3.0168627 3.0528167 2.6807249 3.1998716 3.5732533 4.3876644
## 179 3.5562342 3.5375900 2.9783922 3.3205434 3.4663296 4.6049412
## 180 3.9579215 4.1340430 3.2444222 3.3614624 3.2815491 4.7159041
## 181 4.6756883 4.5693544 3.8430048 3.9605411 3.5714925 5.5001752
## 182 3.4425727 3.6671858 3.2112116 3.4671744 3.6143827 4.7186618
## 183 4.2453364 4.1217517 3.4826004 3.8453621 3.5447782 5.3057171
## 184 3.5933767 3.4401297 3.0628914 3.6329015 3.5564872 5.0705455
## 185 2.8793035 2.7707952 3.1871371 3.7760350 4.1008608 5.0997163
## 186 2.8388629 2.9447155 2.8193912 3.1389949 3.4185423 4.6295220
## 187 5.3436778 5.5164650 4.4457100 4.2750535 3.7545516 5.5772529
## 188 3.7786661 4.1012806 3.2599697 3.2278011 3.5418358 2.5670356
## 189 3.6483251 4.1166558 3.1647255 3.0749347 3.4979327 2.1031489
## 190 4.0931996 4.4142666 3.3732423 3.1967105 3.2893455 2.7122955
## 191 4.0732114 4.5991021 3.4241779 3.0030279 3.0255738 2.4065123
## 192 3.5340533 4.0323600 2.9376004 2.6901586 2.9157429 1.9732127
## 193 4.2199561 4.6860560 3.4274915 3.0563277 2.9935491 2.5319397
## 194 4.0513413 4.6423479 3.5348811 3.1230119 3.3157265 1.5562377
## 195 3.7685564 4.3295218 3.2901121 3.0118962 3.2487240 1.3235146
## 196 6.0997076 6.4075535 5.2917072 4.9452858 4.4716111 3.8714788
## 197 5.2531646 5.5705697 4.6633183 4.4134499 4.1660835 2.5188891
## 198 4.9396751 5.2185802 4.5243420 4.2745496 4.1350299 2.3917803
## 199 5.1854593 5.4756982 4.6469844 4.3860868 4.1059347 2.6228417
## 67 68 69 70 71 72
## 2
## 3
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## 62
## 63
## 64
## 65
## 66
## 67
## 68 3.2439969
## 69 3.2467449 1.0960258
## 70 3.2109419 0.4400981 0.8349648
## 71 4.1879048 1.4663337 2.2490475 1.6906944
## 72 3.9810355 1.1458513 1.5438053 1.2512095 0.9200283
## 73 4.1061429 1.2718829 2.0385054 1.5151609 0.5571333 0.7424370
## 74 4.1264205 1.3451496 2.0708767 1.5786752 0.2935960 0.6827139
## 75 4.2887480 1.8103261 2.4532734 2.0002963 0.8945683 1.1840994
## 76 4.1498724 1.8476003 1.9847887 1.6936598 1.6506318 1.3531688
## 77 4.4541889 2.6594300 2.3874424 2.3552147 2.7318548 2.2958812
## 78 4.1666332 1.9376445 1.9377815 1.7713949 1.8175386 1.3870805
## 79 4.1384204 1.9687586 1.8204012 1.7262684 2.0280941 1.5660670
## 80 4.0569698 1.6372526 1.7046371 1.5355923 1.6375981 1.0928253
## 81 3.3247885 1.7271765 2.4276198 1.7408267 1.8124832 2.0946451
## 82 3.4164462 2.2266832 2.3422772 1.9415042 2.6811004 2.5675626
## 83 3.0047830 1.1828939 1.8008566 1.1725082 1.6806352 1.6766731
## 84 2.9660655 1.3247338 1.5873201 1.1135409 2.0345827 1.8048480
## 85 3.9512303 1.7380955 1.9197108 1.5586899 1.8950061 1.7003325
## 86 4.2063113 2.1835052 2.5087009 2.0215900 2.1461662 2.1595200
## 87 3.8975300 1.7338370 1.6020953 1.5447661 2.0827223 1.5940177
## 88 4.0718101 2.0627660 2.0773008 1.8443016 2.2792270 1.9495151
## 89 4.7973498 3.4085390 3.5040545 3.1609205 3.4159567 3.3984777
## 90 4.6492751 3.0540984 3.3894150 2.9164058 2.8448777 3.0034722
## 91 4.3031582 2.6768125 2.6788434 2.4560139 2.7904914 2.5800250
## 92 4.3877167 2.8428011 2.7980893 2.5924594 3.0038005 2.7745478
## 93 3.6032005 2.5398380 2.6712711 2.3890743 2.3936784 2.2566321
## 94 3.5077820 2.2271349 2.6361381 2.2481066 1.8999850 1.8956362
## 95 3.8024699 2.9867995 2.7814629 2.7135808 3.1202104 2.7669060
## 96 4.3352045 2.5551432 2.8566844 2.4181362 2.4914254 2.4988347
## 97 4.1606334 2.5168294 2.3002772 2.2374283 2.8603957 2.4699864
## 98 5.7696873 4.4839448 4.9277742 4.3792722 4.0938531 4.4652163
## 99 5.6041515 4.1218538 4.8042525 4.1670656 3.5237248 4.0726255
## 100 4.9267006 3.3916621 3.8037379 3.2852547 3.0776855 3.3534089
## 101 5.2300205 3.3984331 3.4341517 3.1801715 3.2391204 3.1261243
## 102 5.1381794 3.2070870 3.3405897 3.0201163 2.9650160 2.9270492
## 103 6.2564211 4.9177431 4.7636792 4.7313526 4.8537725 4.5705192
## 104 5.1311500 3.4299083 3.0592915 3.1310409 3.5894414 3.1440454
## 105 5.2132953 3.5368023 3.2159145 3.2438272 3.6596526 3.2496107
## 106 5.4066208 3.9001430 3.3977261 3.5929787 4.1380374 3.6021982
## 107 5.3741793 3.8650702 3.3185196 3.5663019 4.1090931 3.5457897
## 108 5.2191138 3.5468379 3.2004353 3.2705044 3.6433225 3.2078585
## 109 5.3784876 3.7859938 3.4961175 3.4819567 3.8521674 3.5173559
## 110 5.2625601 3.6538934 3.2407460 3.3499477 3.7971636 3.3501979
## 111 4.7962418 2.7255812 2.5924499 2.5509235 2.6593491 2.2985078
## 112 4.8922132 3.4624155 3.3906390 3.2188066 3.3877350 3.2125491
## 113 4.9988458 3.7884484 3.2983985 3.4855307 4.0460810 3.5262821
## 114 5.0398448 3.8534906 3.3617891 3.5412952 4.0908678 3.5984731
## 115 4.8620532 3.4919517 3.2476097 3.2224892 3.5741932 3.2239796
## 116 4.9311206 3.6809659 3.2122306 3.3897861 3.9078479 3.3818312
## 117 4.6167223 3.0988797 2.8815110 2.8574484 3.1836047 2.8111074
## 118 4.7085409 3.2774547 2.9989301 3.0011945 3.4659310 3.0520153
## 119 4.7301048 3.3311067 2.9484857 3.0898887 3.4978533 2.9790582
## 120 4.5155931 2.9857321 2.6215959 2.7588554 3.2156170 2.6788224
## 121 5.8440479 4.3979128 4.1749596 4.2370760 4.0283335 3.6411635
## 122 5.9974233 4.6424260 4.3671233 4.4382717 4.3242330 3.9337199
## 123 6.1868224 4.9376522 4.5622218 4.7091560 4.6987766 4.2533491
## 124 6.5279965 5.4473281 4.9006019 5.2026518 5.3126316 4.7750168
## 125 6.2243642 5.0018796 4.5965811 4.7641355 4.7993348 4.3312584
## 126 6.0885664 4.7680186 4.4808848 4.5571196 4.4680055 4.0738881
## 127 6.6484463 5.6176441 5.0140324 5.3767747 5.5348760 4.9455963
## 128 6.3569552 4.9588358 4.5021246 4.7125553 4.9209532 4.4167782
## 129 6.4126320 4.9837514 4.6695013 4.7378896 4.7742046 4.4394451
## 130 6.3522524 4.9742122 4.4692447 4.7241984 4.9720997 4.4382454
## 131 6.3353421 4.8530813 4.6068271 4.6114550 4.6260702 4.3332377
## 132 6.2683898 4.7626146 4.5117262 4.5224077 4.5632202 4.2492056
## 133 6.2777703 4.7418034 4.5605966 4.5132564 4.5046174 4.2342752
## 134 6.1902225 4.7067553 4.3205079 4.4611303 4.6481979 4.1886452
## 135 6.4731713 5.1156724 4.6648355 4.8700456 5.0695213 4.5587213
## 136 6.3661518 4.9401367 4.5812425 4.6898937 4.7731715 4.3983209
## 137 6.2886306 4.8457975 4.4422887 4.6051328 4.7379552 4.2840776
## 138 6.3973317 4.9611616 4.6562525 4.7151522 4.7453797 4.4191706
## 139 6.5430995 5.2443780 4.7076637 4.9865217 5.2117278 4.6918368
## 140 6.4441921 5.0583839 4.6522582 4.8106821 4.9211940 4.4998411
## 141 6.6169660 5.3327152 4.8125754 5.0859978 5.2255949 4.7490127
## 142 7.3323548 6.3108922 5.5682996 6.0688770 6.4747671 5.7986392
## 143 8.2860623 7.8514105 7.3917629 7.6690182 7.9706554 7.5379491
## 144 7.2399718 6.7241766 6.2127919 6.5152489 6.8463017 6.3607699
## 145 7.4797745 7.0264096 6.4201166 6.8198820 7.2455086 6.6726228
## 146 7.7082131 7.2222069 6.7735530 7.0236462 7.2024257 6.7857457
## 147 7.3311609 6.7551988 6.4152047 6.5702254 6.7667559 6.3651999
## 148 7.4157202 6.9433139 6.3580232 6.7437951 7.1500196 6.5861705
## 149 7.2674334 6.7519945 6.2263922 6.5596223 6.8967788 6.3746083
## 150 6.9738126 6.3916391 5.9619777 6.1945121 6.4581698 6.0172635
## 151 6.8137100 6.1259743 5.9017912 5.9428499 6.0600848 5.7823575
## 152 6.8661781 6.2143102 5.9118104 6.0271973 6.2793447 5.8889115
## 153 7.8529709 7.2911912 7.0191585 7.1521587 7.3863440 7.0218369
## 154 6.9858473 6.3511640 6.0479092 6.1661033 6.3523383 5.9793073
## 155 7.8887239 7.3252280 7.0951501 7.1659701 7.2799972 7.0200978
## 156 8.4430327 7.9002103 7.7164939 7.7780476 7.7825227 7.5371202
## 157 7.6235035 7.0779667 6.7293402 6.9123162 7.1265605 6.6936942
## 158 6.3940185 5.4878484 5.6901619 5.3530251 5.1236930 5.1780095
## 159 5.7793907 4.9206796 4.8121387 4.7127103 4.8218986 4.5683555
## 160 6.8871985 6.1473499 6.0783067 5.9766212 5.9865952 5.8410154
## 161 6.9717411 6.2388702 6.2325548 6.1015987 6.0884956 5.9567658
## 162 6.9946787 6.0850059 6.4557851 6.0037366 5.5857621 5.8169347
## 163 8.2292970 7.4773509 7.7841277 7.3955681 7.0548376 7.2651113
## 164 8.4665334 7.7252022 8.0569163 7.6508141 7.2294982 7.5019205
## 165 5.4749848 4.6087663 4.3654069 4.3922938 4.6136595 4.2501943
## 166 5.8154271 4.9693846 4.8353803 4.7788979 4.8462788 4.5603724
## 167 7.2471279 6.3844150 6.7320964 6.2892147 5.8572082 6.1117598
## 168 5.6384627 4.7631429 4.5902365 4.5990186 4.6564431 4.3105564
## 169 5.7557143 4.9174877 4.7546852 4.7067458 4.7766283 4.5063658
## 170 5.6638451 4.8170883 4.6420035 4.5988480 4.6798713 4.4167766
## 171 5.6483194 4.8757714 4.5167739 4.6419531 4.8988550 4.4625348
## 172 5.5779871 4.7695721 4.4632660 4.5323303 4.7950048 4.3965059
## 173 4.6123966 3.5400152 3.0987568 3.2587436 3.9944882 3.4578363
## 174 4.5787924 3.3617517 3.2671891 3.1080857 3.5227397 3.2891083
## 175 4.2670257 2.9130989 2.7552228 2.6962594 3.2161345 2.8301250
## 176 4.2891712 2.6062656 3.1073281 2.6254655 2.3369205 2.5116408
## 177 3.9436850 2.3003839 2.3218859 2.1687085 2.5405636 2.2331029
## 178 4.3280050 2.9300221 2.9841104 2.7130226 3.1113009 2.9320126
## 179 4.7051784 3.3943202 3.5893353 3.2208118 3.3150616 3.3337038
## 180 5.0072956 3.5003471 3.9414906 3.4365019 3.1998175 3.4202874
## 181 5.7922783 4.5931570 4.9096964 4.4612234 4.2718367 4.5069309
## 182 4.7124872 3.1949919 3.3777887 3.0874199 3.2134629 3.0872696
## 183 5.5065169 4.2656352 4.5261067 4.0966694 4.1153103 4.2252483
## 184 5.0842555 3.7996267 3.8932958 3.5745292 3.8746270 3.7843379
## 185 4.6885267 3.4437191 3.0683938 3.1644998 3.8907627 3.3816614
## 186 4.4410494 2.9378902 2.8541493 2.7371038 3.1405511 2.8352018
## 187 6.0995126 4.8097879 5.3936119 4.8121901 4.3098133 4.7498420
## 188 2.9559857 3.1942643 3.6117628 3.1770156 3.4148876 3.5658906
## 189 2.6006847 2.8308745 3.3524810 2.8746491 3.1478167 3.3151392
## 190 3.3110043 3.4611517 3.9921969 3.4687873 3.5621383 3.8580041
## 191 3.1259747 3.2233688 3.8786116 3.3203552 3.4383962 3.7673751
## 192 2.5669462 2.8072474 3.3615566 2.8441322 3.2365751 3.4474170
## 193 3.3349007 3.4096379 4.0893522 3.4865357 3.5623868 3.9509780
## 194 2.4346157 3.1781892 3.7948804 3.3053654 3.4677957 3.7579200
## 195 2.1229920 3.0060658 3.5605693 3.0942368 3.4264502 3.6283818
## 196 4.7143147 5.6419312 6.2424427 5.7031185 5.6885843 6.0998501
## 197 3.2328124 4.8526244 5.2813268 4.8715959 5.2458216 5.4865622
## 198 2.8453003 4.6773675 4.9711298 4.6691090 5.1583502 5.2898796
## 199 3.2232338 4.8709584 5.2476233 4.8738046 5.2856390 5.4896747
## 73 74 75 76 77 78
## 2
## 3
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## 74 0.4194399
## 75 0.9419931 0.8940489
## 76 1.6566579 1.6226845 1.4588431
## 77 2.7379503 2.6939649 2.5907701 1.1654828
## 78 1.7745584 1.7500887 1.5543552 0.3505725 1.0791085
## 79 2.0439362 1.9709934 1.9288487 0.6235593 0.8935161 0.6117702
## 80 1.4451925 1.5129283 1.3397234 0.6837027 1.5535858 0.5728722
## 81 1.9979717 1.9373186 2.2171271 2.1362276 2.7670760 2.3257587
## 82 2.7543812 2.7343691 2.9666328 2.0959866 2.0899114 2.2232301
## 83 1.7001679 1.6996105 2.0479874 1.9149403 2.5630302 2.0356656
## 84 1.9885166 2.0132164 2.3372858 1.8192291 2.2264447 1.9012739
## 85 1.9595880 1.9030071 2.1972954 1.5837130 1.9327738 1.6507927
## 86 2.2640636 2.2261437 2.4212219 1.7866803 2.0493871 1.9171532
## 87 2.0420139 1.9931043 2.2757795 1.6845987 1.9405307 1.6080929
## 88 2.2195001 2.2473047 2.4104591 1.6557695 1.7822722 1.6215631
## 89 3.5325848 3.5064599 3.5178340 2.5953859 2.3093291 2.6831848
## 90 3.0424254 2.9724236 2.9693554 2.4010554 2.4966470 2.5257250
## 91 2.8191954 2.8016167 2.8225996 2.0068222 1.8993389 1.9846284
## 92 3.0153226 3.0157904 3.0338258 2.1247127 1.8892206 2.1035713
## 93 2.4369436 2.4140750 2.3004000 1.6119815 1.8221736 1.6407852
## 94 1.8814369 1.9043771 1.7337601 1.7490499 2.4326790 1.7878574
## 95 3.1036544 3.0991184 3.0300404 1.9553252 1.5504894 1.8932612
## 96 2.6151924 2.5556009 2.6458254 2.0684323 2.2213670 2.1517638
## 97 2.8372542 2.8223761 2.9334146 1.9991108 1.7462643 1.9174928
## 98 4.4220829 4.2944944 4.2835015 3.8382509 3.8463324 4.0174326
## 99 3.8884025 3.7414649 3.7179986 3.7999727 4.2004062 3.9859509
## 100 3.3597827 3.2432980 3.2621814 2.8053729 2.9157470 2.9559113
## 101 3.3525592 3.2955875 3.1643434 2.2366236 1.8962039 2.2464068
## 102 3.0863012 3.0377651 2.8925927 2.0683589 1.9250370 2.1123881
## 103 4.9144171 4.7949798 4.8700393 4.0755272 3.6863504 4.0670733
## 104 3.5617422 3.5446445 3.4662495 2.3322391 1.6415234 2.1866864
## 105 3.6341705 3.6256362 3.5238244 2.3995157 1.7072884 2.2646548
## 106 4.0791183 4.0644524 3.9764141 2.8565135 2.0582633 2.6544582
## 107 4.0612708 4.0246459 3.9492130 2.8678563 2.1030878 2.6486926
## 108 3.6258533 3.5964549 3.4839574 2.4171819 1.7563721 2.2497127
## 109 3.8797522 3.8487361 3.7485288 2.5823346 1.8196474 2.4910817
## 110 3.8010851 3.7544099 3.6787797 2.5331185 1.7613254 2.3808470
## 111 2.6677998 2.6111214 2.4951129 1.7538976 1.7124843 1.6090185
## 112 3.4756381 3.4245938 3.1158389 2.0450244 1.5447730 2.0225672
## 113 3.9936939 3.9753140 3.7387594 2.5785419 1.7522100 2.3724136
## 114 4.0738737 4.0332859 3.8123958 2.6176027 1.7401832 2.4329544
## 115 3.5490832 3.5504614 3.2484485 2.1269218 1.4977498 2.0015690
## 116 3.8644794 3.8256290 3.6146873 2.4600381 1.6636805 2.2652126
## 117 3.1681275 3.1475768 2.8392501 1.7847707 1.3345278 1.6385035
## 118 3.3930161 3.4215120 3.1412983 2.0067104 1.4187496 1.8651071
## 119 3.4533701 3.4040227 3.1628456 2.1509734 1.6030846 1.9395564
## 120 3.1053984 3.1153387 2.8294484 1.8998015 1.5773589 1.6607937
## 121 3.9805237 3.9644880 3.7781097 3.0960465 2.8328395 2.9521436
## 122 4.2921278 4.2719526 4.1042032 3.2566619 2.8096044 3.1250348
## 123 4.6788936 4.6362364 4.4890253 3.5728277 2.9911274 3.4165629
## 124 5.3042391 5.2208920 5.1157614 4.1884397 3.5177919 3.9906596
## 125 4.7588307 4.7304021 4.5846156 3.6448813 3.0365355 3.4808921
## 126 4.4381196 4.4181658 4.2415390 3.3760755 2.8831890 3.2375020
## 127 5.5005935 5.4212522 5.3265356 4.4301162 3.7707995 4.2099027
## 128 4.8411172 4.8386360 4.5700405 3.6151379 2.9882505 3.4237157
## 129 4.7983560 4.7545781 4.4614180 3.4715654 2.8309036 3.3548309
## 130 4.8835857 4.8796387 4.6288486 3.6761203 3.0528269 3.4757000
## 131 4.6455931 4.6197272 4.3226168 3.3308175 2.7347907 3.2456650
## 132 4.5621640 4.5486370 4.2540403 3.2669833 2.6892890 3.1761298
## 133 4.5194110 4.5029034 4.2023125 3.2388111 2.6961834 3.1716471
## 134 4.5813983 4.5822634 4.3229058 3.3407103 2.7439414 3.1881216
## 135 5.0212806 4.9722013 4.7975901 3.8061010 3.1546704 3.6574370
## 136 4.7916902 4.7408719 4.4698303 3.4676029 2.8108062 3.3389853
## 137 4.6990917 4.6718140 4.4026561 3.4412730 2.8239374 3.2749143
## 138 4.7666806 4.7277291 4.4347967 3.4425676 2.8125311 3.3327515
## 139 5.1680218 5.1271303 4.8844947 3.9109325 3.2226361 3.7096902
## 140 4.9183959 4.8715466 4.5923670 3.6171871 2.9503675 3.4545203
## 141 5.2424066 5.1540277 4.9152940 3.9790381 3.3074619 3.7882379
## 142 6.3962837 6.3300346 6.1631690 5.3187403 4.6547185 5.0539345
## 143 7.9169639 7.8845377 7.6094068 6.9841922 6.5583437 6.8278490
## 144 6.7945153 6.7530702 6.4288390 5.6891295 5.1710269 5.5058364
## 145 7.1415220 7.1185123 6.8246404 6.1139662 5.6055055 5.8976880
## 146 7.2459650 7.1163402 6.8786758 6.1202391 5.5779257 5.9917339
## 147 6.7263137 6.6778811 6.4049305 5.6770628 5.2217645 5.5681363
## 148 7.0554123 7.0250107 6.7294063 6.0354218 5.5407678 5.8223207
## 149 6.8342484 6.7836352 6.4816869 5.7903919 5.3042671 5.5956889
## 150 6.4061042 6.3729031 6.0347886 5.3122253 4.8456566 5.1548019
## 151 6.0511369 6.0321371 5.6359181 4.9357460 4.5388142 4.8464029
## 152 6.1840116 6.2077703 5.8415043 5.1338996 4.7257096 5.0091536
## 153 7.2558562 7.3033372 7.0000621 6.5010057 6.2549269 6.3868237
## 154 6.3128600 6.2815352 5.9534264 5.2302908 4.7927225 5.1203135
## 155 7.2727017 7.2432898 6.9445480 6.3575665 6.0326240 6.2853100
## 156 7.8028897 7.7227487 7.5106905 7.0132201 6.7518060 6.9646274
## 157 7.0558362 7.0128582 6.7911580 6.1292335 5.7340413 6.0206629
## 158 5.2477019 5.2108872 4.7892121 4.1827844 3.9455740 4.2356317
## 159 4.7768835 4.8111572 4.3991356 3.5280869 3.0778393 3.4666138
## 160 6.0028758 6.0009678 5.5875392 4.9168352 4.5926064 4.8924360
## 161 6.0822612 6.0946425 5.7736952 5.2300920 5.0109548 5.2110930
## 162 5.7809957 5.7226583 5.3136756 4.9227098 4.8460253 5.0293592
## 163 7.2385497 7.1806060 6.8549578 6.5009112 6.4028896 6.5941625
## 164 7.4692423 7.3759752 7.0618367 6.7378481 6.6577656 6.8496588
## 165 4.5494413 4.5706497 4.1755838 3.2932237 2.8342604 3.1778755
## 166 4.8480399 4.8084511 4.4881178 3.6475323 3.2123750 3.5976236
## 167 6.1023496 6.0078288 5.6258762 5.1868722 5.0531352 5.3037975
## 168 4.6382712 4.5861850 4.2754345 3.5335618 3.1946593 3.4523542
## 169 4.8018435 4.7574399 4.4000287 3.4928137 2.9816982 3.4338522
## 170 4.7082614 4.6681010 4.2983424 3.3703159 2.8551763 3.3120272
## 171 4.8543710 4.8241466 4.5192332 3.5627847 2.9884964 3.4388340
## 172 4.7333047 4.7398236 4.3893499 3.4267356 2.8707580 3.3113170
## 173 3.8896323 3.9088964 3.8450705 2.8787970 2.3245523 2.6940283
## 174 3.5430173 3.5363824 3.4301192 2.4815872 2.0786715 2.4390726
## 175 3.1206058 3.1613898 3.0626084 2.2781818 2.0941110 2.1562543
## 176 2.4432656 2.4121667 2.2533339 2.2584225 2.7902453 2.3326702
## 177 2.4871312 2.4883898 2.4394082 1.9419384 2.1700459 1.8739366
## 178 3.1008638 3.1309645 3.0468404 2.2260964 2.0996362 2.2339360
## 179 3.4513064 3.4009257 3.2782471 2.5710721 2.4522016 2.6338493
## 180 3.3946679 3.3302237 3.3476115 3.0478845 3.2167870 3.1464555
## 181 4.5590054 4.4315116 4.4356093 3.9017852 3.7703934 4.0173159
## 182 3.2530049 3.2308548 3.2697629 2.8342797 2.8601539 2.8025685
## 183 4.2878319 4.2378356 4.2433934 3.5809274 3.3743403 3.6700022
## 184 3.9325399 3.9372159 3.9735718 3.1426155 2.8150277 3.1730333
## 185 3.7998720 3.8159286 3.9235235 2.9961978 2.5014094 2.8505733
## 186 3.1755522 3.1191111 3.2502042 2.5329772 2.3515928 2.4653764
## 187 4.6358208 4.5020633 4.4997145 4.4239629 4.6443877 4.5804014
## 188 3.5534083 3.4930853 3.3280710 3.2069467 3.5279110 3.2916075
## 189 3.2302418 3.2075546 3.0929403 3.1445150 3.6398620 3.2500142
## 190 3.7769707 3.6889987 3.5637749 3.5098536 3.8820475 3.6554631
## 191 3.6341758 3.5469142 3.5528070 3.7221281 4.2828665 3.9002611
## 192 3.3577384 3.3172802 3.3345139 3.3316636 3.8407521 3.4974287
## 193 3.7732687 3.7002974 3.6877633 3.8122794 4.3526734 4.0139994
## 194 3.6061684 3.5471473 3.7116784 3.9825877 4.5831624 4.1243712
## 195 3.5135264 3.4823083 3.6649974 3.8120185 4.3566448 3.9455629
## 196 5.9440811 5.8406476 5.8667858 5.9765937 6.3249745 6.1423906
## 197 5.3982132 5.3401073 5.3964865 5.3764342 5.7164156 5.5294460
## 198 5.3060010 5.2167310 5.3110624 5.2019220 5.4685153 5.3269571
## 199 5.4497205 5.3727810 5.4359815 5.3643026 5.6537064 5.5062199
## 79 80 81 82 83 84
## 2
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## 80 0.9561883
## 81 2.3667646 2.3823590
## 82 2.0788328 2.4479782 1.4191629
## 83 2.1059084 1.9874649 0.7274435 1.4352243
## 84 1.9026113 1.9077781 1.1242704 1.0673286 0.6015669
## 85 1.6433094 1.7971588 1.5648576 1.4963861 1.3749576 1.2615134
## 86 1.9407594 2.1428107 1.4923951 1.3648759 1.5773688 1.4948166
## 87 1.6295222 1.6792328 2.0470633 1.9251185 1.6404545 1.4590888
## 88 1.7523505 1.7807429 1.9840809 1.6474411 1.6980276 1.4398314
## 89 2.6615237 3.0527515 2.5775523 1.8493495 2.7356203 2.4969852
## 90 2.5763754 2.8479088 2.0271097 1.8859598 2.3176535 2.2875705
## 91 2.0791825 2.2727233 2.2763190 1.7978579 2.1628747 1.9213018
## 92 2.1710960 2.4045150 2.4327832 1.7960472 2.3256353 2.0307427
## 93 1.7685341 1.8751758 2.0710915 1.8958944 1.9613770 1.8355950
## 94 2.0854768 1.7693195 1.9582234 2.3855184 1.7837286 1.9074876
## 95 1.8615191 2.2001290 2.6959594 1.9685047 2.5021853 2.1528114
## 96 2.2473188 2.4201787 1.8249790 1.7206433 1.9281691 1.8506379
## 97 1.9297723 2.1768421 2.4226483 1.7818015 2.1695837 1.8222592
## 98 3.9705041 4.3898189 3.1061916 3.0676067 3.6739448 3.7316649
## 99 4.0482910 4.2285370 2.7909605 3.4096750 3.3917019 3.6701274
## 100 2.9608039 3.2979983 2.1685987 2.1801899 2.6184804 2.6669109
## 101 2.2528776 2.6582229 2.8038733 2.2786616 2.8764020 2.6751900
## 102 2.1821210 2.4963977 2.5811423 2.2030189 2.6761010 2.5296813
## 103 4.0680835 4.3601675 4.7806393 4.2987024 4.6892303 4.4238532
## 104 2.1583680 2.5376466 3.3840917 2.5935817 3.1665330 2.7963074
## 105 2.2687430 2.6261030 3.4107557 2.6153097 3.2235180 2.8587369
## 106 2.6171472 2.9777928 3.9501078 3.1107107 3.6825911 3.2820049
## 107 2.5882958 2.9642289 3.9776657 3.1890785 3.6899259 3.3057052
## 108 2.2734023 2.6124935 3.4630858 2.7428928 3.2542502 2.9114754
## 109 2.4435842 2.9077266 3.4966638 2.6234555 3.3936744 3.0329184
## 110 2.3094027 2.7659502 3.5694838 2.7479291 3.3728591 3.0023446
## 111 1.7575072 1.8819568 2.7508832 2.4913072 2.5179448 2.3434877
## 112 2.0289646 2.4763579 3.0566860 2.4492757 3.0566501 2.8150406
## 113 2.3258274 2.7129370 3.8980330 3.0985457 3.6343757 3.2511096
## 114 2.3307945 2.8108142 3.8996007 3.0631618 3.6715674 3.2892262
## 115 2.0841789 2.3805719 3.3896488 2.6945462 3.2191112 2.8955625
## 116 2.2336788 2.6138501 3.8167690 3.0640996 3.5467687 3.1681433
## 117 1.7126809 1.9991686 3.0903896 2.5533810 2.8923842 2.6176187
## 118 1.9330618 2.1791668 3.3187590 2.6292717 3.0890238 2.7458262
## 119 1.9866830 2.2516371 3.5264047 2.9781885 3.2376167 2.9255328
## 120 1.7878475 1.8625925 3.3275932 2.8677098 2.9776323 2.6906185
## 121 3.0220992 3.1377693 4.4609791 4.1105247 4.2555260 4.0605635
## 122 3.1455467 3.3744147 4.6273455 4.1188704 4.4470720 4.1965294
## 123 3.3747822 3.6934650 4.9436812 4.3470429 4.7506644 4.4669726
## 124 3.8833446 4.2690852 5.5837260 4.9323623 5.3364659 5.0267500
## 125 3.4472956 3.7470489 5.0432471 4.4099025 4.8293377 4.5269150
## 126 3.2500807 3.4989230 4.7250249 4.1878685 4.5525877 4.2938294
## 127 4.1156303 4.4557249 5.8550193 5.2112384 5.5617756 5.2436902
## 128 3.4210112 3.6624995 5.1561051 4.5032926 4.8968515 4.5776600
## 129 3.3204224 3.7055384 4.8751133 4.2231819 4.7620887 4.4831113
## 130 3.4575597 3.6967980 5.2403317 4.5806162 4.9543867 4.6287084
## 131 3.2218067 3.5882070 4.6967520 4.0567798 4.6113258 4.3397915
## 132 3.1571932 3.4950489 4.6542011 4.0222609 4.5480389 4.2728412
## 133 3.1548666 3.4989714 4.5520290 3.9562631 4.4883193 4.2316278
## 134 3.1590647 3.4335034 4.8488490 4.2063773 4.6273990 4.3176120
## 135 3.6101842 3.9205716 5.3167808 4.6540428 5.0722701 4.7356045
## 136 3.2732461 3.6783482 4.8978904 4.2381480 4.7594507 4.4715913
## 137 3.2556991 3.5532192 4.9583819 4.3307763 4.7441412 4.4443731
## 138 3.3067378 3.6811318 4.8511481 4.1978492 4.7391413 4.4595512
## 139 3.6579063 3.9823770 5.4474693 4.7583850 5.1872153 4.8614655
## 140 3.4116088 3.7752422 5.0796057 4.4249807 4.9031432 4.6083961
## 141 3.7052308 4.1037603 5.4631240 4.8199429 5.2442738 4.9505850
## 142 4.9458408 5.2368208 6.7822621 6.1277425 6.4143322 6.0825392
## 143 6.7876073 6.9697427 8.0699061 7.5709289 7.8281131 7.5850702
## 144 5.4513145 5.6862138 6.9396343 6.3738545 6.6794759 6.4043838
## 145 5.8539795 6.0200056 7.4261100 6.8546924 7.0834534 6.7888055
## 146 5.9099203 6.2580121 7.2989477 6.7590482 7.1174111 6.8527514
## 147 5.5735467 5.7640655 6.8584482 6.3439860 6.6572048 6.3849306
## 148 5.7727119 5.9470361 7.3251677 6.7790238 6.9940930 6.7104312
## 149 5.5418506 5.7498652 7.0465675 6.5294063 6.7575717 6.4898504
## 150 5.1360434 5.3346058 6.5614743 6.0328357 6.3228659 6.0591972
## 151 4.8531983 5.0662609 6.0178663 5.5423130 5.9098094 5.6915363
## 152 5.0460399 5.1548893 6.3137259 5.8024486 6.1032032 5.8411041
## 153 6.4556038 6.4389799 7.5241409 7.1439229 7.2817578 7.0684854
## 154 5.1263566 5.3172966 6.3963770 5.8956218 6.2180378 5.9622758
## 155 6.2842820 6.4609661 7.2928771 6.8763010 7.1768559 6.9796029
## 156 6.9817742 7.1377297 7.9054264 7.5928915 7.7918254 7.6166531
## 157 6.0434989 6.1666862 7.3028537 6.8347817 7.0582274 6.7878417
## 158 4.2630572 4.5581726 4.7877893 4.5179459 5.0079332 4.9155432
## 159 3.5476373 3.7276885 4.7448233 4.1935861 4.6667869 4.4104659
## 160 4.9262732 5.1284049 5.8429200 5.4074353 5.8344022 5.6477765
## 161 5.2757524 5.3920751 6.0294406 5.7030075 6.0140395 5.8601257
## 162 5.0565034 5.3381797 5.1626075 5.1047284 5.5268542 5.5376394
## 163 6.5916897 6.8670560 6.6548142 6.5673597 6.9808843 6.9835059
## 164 6.8258910 7.1521423 6.8139104 6.7688958 7.1951019 7.2271528
## 165 3.1986356 3.4007254 4.6523491 4.1050164 4.4838409 4.2179319
## 166 3.6226483 3.8743222 4.8622614 4.3770879 4.7757746 4.5290841
## 167 5.2859200 5.6585548 5.3817263 5.2827591 5.7897728 5.7978515
## 168 3.4954699 3.6766729 4.8296363 4.4422520 4.6732485 4.4476296
## 169 3.4378943 3.7577203 4.7429857 4.1980126 4.6781038 4.4256780
## 170 3.3041627 3.6410724 4.6446378 4.0826657 4.5799066 4.3279494
## 171 3.4207629 3.6970725 5.0096787 4.3927064 4.8005304 4.4901220
## 172 3.3147909 3.5595953 4.8414941 4.2134480 4.6550089 4.3501461
## 173 2.6899163 2.9071523 3.6399373 2.9066439 3.3274908 2.9412512
## 174 2.4764743 2.7731832 2.9294496 2.2440873 2.8632472 2.5680741
## 175 2.2989656 2.3331035 2.8962896 2.4270021 2.6241412 2.3398741
## 176 2.5762286 2.4405945 2.0476816 2.5091758 2.1243595 2.2838767
## 177 2.0290293 1.9621190 2.3845035 2.2985298 2.0998039 1.9711438
## 178 2.3150573 2.4769482 2.5351051 2.0343423 2.4625484 2.2198242
## 179 2.6737280 2.9779665 2.5646135 2.2133993 2.7426203 2.6189673
## 180 3.2413655 3.4048280 2.3571846 2.5045259 2.7042423 2.7741355
## 181 3.9703029 4.4069635 3.2872472 3.0995976 3.7485071 3.7401770
## 182 2.9058897 2.9946443 2.6047576 2.5200448 2.6060363 2.5291222
## 183 3.6606497 4.0203474 3.1110570 2.7216018 3.4514942 3.3449136
## 184 3.1738110 3.4850751 2.9640209 2.3130988 3.0910523 2.8490282
## 185 2.8156968 3.0546147 3.3961640 2.6454005 3.1154201 2.7232173
## 186 2.4514490 2.7094182 2.5804288 2.1658313 2.4485807 2.2221837
## 187 4.5974903 4.8521251 3.4583995 3.8445401 4.0209693 4.2165274
## 188 3.3727729 3.4284497 2.2927118 2.6207594 2.4758905 2.5978544
## 189 3.3607069 3.2735512 2.1624804 2.6927309 2.2525040 2.4409962
## 190 3.6811071 3.8064471 2.3547549 2.8138334 2.7197078 2.9139928
## 191 3.8779463 3.9217748 2.4314343 3.1658455 2.7347710 3.0260245
## 192 3.4710760 3.5022654 2.1731295 2.6979289 2.3422802 2.5390096
## 193 3.9933364 4.0619167 2.4611491 3.1519435 2.8479156 3.1302283
## 194 4.1588932 4.0850653 2.4399381 3.2429129 2.6038155 2.9258091
## 195 3.9772407 3.9016885 2.3464922 3.0007914 2.4309349 2.6762408
## 196 6.1155637 6.2698611 4.3619839 4.8980049 4.8293325 5.0789993
## 197 5.4589030 5.5777310 4.0651100 4.3970061 4.2999230 4.4479269
## 198 5.2223986 5.3890876 4.0409873 4.2637795 4.1846183 4.2751254
## 199 5.4078890 5.5749865 4.0885338 4.3657882 4.3159740 4.4423150
## 85 86 87 88 89 90
## 2
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## 85
## 86 0.7090467
## 87 0.7423311 1.3802145
## 88 0.7383552 0.9665519 0.8270095
## 89 1.9117779 1.4428416 2.3917779 1.7848578
## 90 1.5894711 1.0266290 2.1618222 1.6915342 0.9990823
## 91 1.1716622 1.0944104 1.3746312 0.8181816 1.2140468 1.2465453
## 92 1.3612719 1.2231547 1.5705774 0.9547487 1.0617089 1.3209338
## 93 2.0622710 2.0742872 2.2136914 2.0259588 2.5696722 2.4321291
## 94 2.2182443 2.3090970 2.3140572 2.2504925 3.1522777 2.7626410
## 95 2.3345556 2.3747213 2.3634885 2.1360790 2.5174634 2.7115154
## 96 1.1627001 0.7319296 1.6266822 1.1683205 1.4006269 0.8983158
## 97 1.1623194 1.3406265 1.1005825 0.7418024 1.6386009 1.7804856
## 98 3.2239448 2.6240070 3.8299728 3.4478848 2.3038467 1.8927353
## 99 3.1981298 2.7120646 3.7535089 3.5347212 3.0786428 2.2192535
## 100 2.0441919 1.4747777 2.6328119 2.2658930 1.5210346 0.7974308
## 101 2.2899306 2.0492374 2.5232133 2.1564573 2.0118451 2.0613180
## 102 2.1576073 1.8970256 2.4492558 2.0559842 1.9782036 1.9313643
## 103 4.3021383 4.2442204 4.3190804 4.1201882 4.2048009 4.3927319
## 104 2.5012884 2.5759186 2.3974683 2.1639561 2.5229081 2.8521724
## 105 2.5626762 2.5750657 2.4987385 2.1935776 2.4486594 2.7964580
## 106 3.0017048 3.1206649 2.7679095 2.6047380 3.0090967 3.3767678
## 107 3.0068418 3.1883267 2.7153136 2.6563728 3.1630259 3.4726663
## 108 2.5873619 2.6529019 2.4521093 2.2258818 2.6059358 2.8798904
## 109 2.7029032 2.6345716 2.7384929 2.3911413 2.2966848 2.7317440
## 110 2.6713875 2.7508736 2.5499941 2.3663055 2.6239314 2.9699697
## 111 1.9960025 2.1870365 1.8619694 1.8197205 2.6687529 2.5800637
## 112 2.3339989 2.1806638 2.5098349 2.1452998 1.7521902 1.9838147
## 113 2.8776870 3.0130921 2.6547171 2.5064254 2.7513611 3.1248530
## 114 2.8883025 3.0098520 2.7045244 2.5710371 2.6836534 3.0817349
## 115 2.5066765 2.4950581 2.4916086 2.1264182 2.1371544 2.4965989
## 116 2.8116514 2.9535608 2.5898413 2.4528033 2.7571746 3.0937393
## 117 2.1886243 2.2684097 2.1153015 1.8994591 2.2285764 2.3736341
## 118 2.4038044 2.4493937 2.3365981 2.0127451 2.2542558 2.5770216
## 119 2.5540192 2.7419919 2.2911826 2.2313506 2.7893226 2.9377245
## 120 2.3510872 2.6040364 2.0557668 2.0083674 2.7896195 2.8928212
## 121 3.7536671 3.8672413 3.5978818 3.5434821 4.0730022 4.1309929
## 122 3.8850671 3.9507573 3.7684574 3.6441438 3.9749641 4.1573470
## 123 4.1360991 4.2306418 3.9671372 3.8958128 4.1947573 4.4219849
## 124 4.6830612 4.8806749 4.3990998 4.4658656 4.8357982 5.0930153
## 125 4.2137034 4.3153438 4.0322227 3.9433982 4.2486403 4.5177858
## 126 3.9727637 4.0248034 3.8511669 3.7189912 4.0110625 4.2062833
## 127 4.9225004 5.1645036 4.5774873 4.6840777 5.1576676 5.4147867
## 128 4.3917973 4.5201146 4.1764437 4.0814000 4.4342900 4.7335816
## 129 4.2266089 4.2315397 4.1774299 3.9969407 3.9821576 4.2834867
## 130 4.4506729 4.6182966 4.2061095 4.1489982 4.5540088 4.8625932
## 131 4.1068438 4.0632311 4.1154543 3.8814059 3.8114745 4.1102066
## 132 4.0583836 4.0281800 4.0513623 3.8242091 3.8235187 4.1121008
## 133 4.0155554 3.9335399 4.0500450 3.7986975 3.7434672 3.9873232
## 134 4.1452969 4.2323049 3.9980223 3.8744065 4.1686377 4.4499245
## 135 4.5878083 4.6984971 4.3980155 4.3151330 4.6246438 4.9295325
## 136 4.2194680 4.2636783 4.1341800 4.0048360 4.0660305 4.3580176
## 137 4.2351023 4.3345251 4.0683888 3.9678701 4.2426898 4.5144897
## 138 4.2114511 4.2103306 4.1751783 3.9779958 3.9494237 4.2629628
## 139 4.6373917 4.8073873 4.3914644 4.3615792 4.6723261 4.9972385
## 140 4.3552632 4.4344582 4.2076828 4.1064100 4.2610167 4.5470324
## 141 4.6742172 4.8502362 4.4414996 4.4658851 4.7173829 4.9925903
## 142 5.8681572 6.1893580 5.4125710 5.6167612 6.2182753 6.4748437
## 143 7.2745883 7.4527275 7.0195955 7.0712136 7.1726036 7.4007289
## 144 6.0291013 6.2237407 5.7394765 5.7978031 5.8923691 6.1452270
## 145 6.4630949 6.7330225 6.0819435 6.1985184 6.4934942 6.7587438
## 146 6.4781410 6.6137127 6.2672365 6.3127929 6.2364883 6.4734402
## 147 6.0940925 6.1601837 5.9313087 5.8376602 5.7959582 6.0515426
## 148 6.3760416 6.6406906 5.9975951 6.1278659 6.4282408 6.6608942
## 149 6.1327394 6.3609520 5.7940319 5.9094764 6.1384774 6.3368659
## 150 5.6977782 5.8486255 5.4632923 5.4570407 5.5018326 5.7473422
## 151 5.3031296 5.2972309 5.2415917 5.0903742 4.8264409 5.0368850
## 152 5.5350979 5.5860583 5.3805741 5.2389770 5.2137484 5.4640234
## 153 6.8611032 6.9576053 6.6868987 6.5960814 6.7494918 6.9402906
## 154 5.6323536 5.6795077 5.4908887 5.3839075 5.2984960 5.5279449
## 155 6.6767596 6.7015199 6.6077464 6.5046286 6.3302467 6.5264184
## 156 7.3682010 7.3954185 7.2955556 7.2237326 7.1408898 7.2695149
## 157 6.5627141 6.6627305 6.3661372 6.3008297 6.4054786 6.6408307
## 158 4.5244272 4.1493909 4.7926270 4.4295693 3.7314904 3.6676934
## 159 4.0951990 3.9496816 4.1402907 3.7753488 3.5031193 3.7737382
## 160 5.2759993 5.1405241 5.3599261 5.0806896 4.5600668 4.7696064
## 161 5.6183154 5.4837208 5.6896627 5.4305237 5.2168401 5.3269585
## 162 5.1521352 4.6923199 5.5218641 5.1671988 4.3503983 4.1090194
## 163 6.6575895 6.2761806 6.9848872 6.6859446 5.9396391 5.7949340
## 164 6.8705641 6.4797527 7.2351677 6.9585621 6.1189951 5.9425795
## 165 3.8804185 3.8913928 3.8009626 3.6048814 3.6221223 3.8514027
## 166 4.2242053 4.1355020 4.2272227 3.9875753 3.8480172 4.0279501
## 167 5.3801634 4.9116253 5.7757505 5.4390254 4.4797465 4.2658985
## 168 4.1538251 4.1690373 4.0649091 3.9364594 4.0703735 4.1673202
## 169 4.0616077 3.9681892 4.0810332 3.8303666 3.5640160 3.7924537
## 170 3.9474962 3.8670101 3.9768666 3.7292295 3.4339304 3.6853489
## 171 4.1773457 4.2451763 4.0423301 3.9017499 3.9502988 4.2511933
## 172 4.0327526 4.0534718 3.9431129 3.7342679 3.7074915 4.0243011
## 173 2.4895193 2.6455780 2.1885457 2.0353246 2.5458965 2.8306709
## 174 1.9669864 1.7960757 2.1094652 1.6153633 1.2595655 1.6117276
## 175 1.8148052 1.9109365 1.6782838 1.3355481 2.0045508 2.0989629
## 176 1.6892183 1.5414640 1.9993924 1.7758152 2.2169990 1.4940411
## 177 1.3474550 1.6144048 1.2332749 1.1836539 2.1950643 1.9561366
## 178 1.6490878 1.4491990 1.8863044 1.3465632 1.3030823 1.4195917
## 179 1.9681846 1.5404880 2.3613645 1.8947803 1.1332170 0.9245312
## 180 2.1476862 1.6189254 2.6167941 2.2323325 1.8695063 1.1086021
## 181 3.1345276 2.5850466 3.6309189 3.2672390 2.1695481 1.8265232
## 182 1.9095906 1.7193330 2.0031261 1.7554304 2.1951609 1.7619029
## 183 2.7940486 2.2043011 3.2533757 2.7520366 1.6953690 1.5661488
## 184 2.3129765 1.8398846 2.6441140 2.0713808 1.3271167 1.5352607
## 185 2.2441223 2.3530424 1.9865867 1.8073401 2.4069459 2.6455628
## 186 1.4879750 1.5309910 1.4351065 1.3158225 1.9220493 1.7694059
## 187 3.7151773 3.2002899 4.2247412 3.9826596 3.3527005 2.6280592
## 188 2.9114510 2.7761847 3.1711536 3.0543068 3.1041875 2.6516590
## 189 2.8966983 2.8423204 3.1397497 3.0716772 3.3755809 2.9043586
## 190 3.1804886 2.9630169 3.5600394 3.4459305 3.2813517 2.7531361
## 191 3.4040968 3.3076408 3.7510556 3.7990141 3.9556592 3.3556572
## 192 3.0343581 2.9925479 3.3580192 3.3674961 3.5757601 3.1297199
## 193 3.4912685 3.3172264 3.9136794 3.8796257 3.8537461 3.2820499
## 194 3.5170567 3.5287810 3.7834129 3.8669331 4.2586910 3.7186988
## 195 3.3533254 3.3715442 3.6014221 3.6469594 4.0648084 3.6105677
## 196 5.4456662 5.1665417 5.8469853 5.7718226 5.4354305 4.8940948
## 197 4.9747446 4.8761307 5.2891419 5.2797478 5.1409484 4.8107294
## 198 4.8119067 4.7959500 5.0440766 5.1090414 5.0749771 4.7943409
## 199 4.9459309 4.8618167 5.2363595 5.2583562 5.1175840 4.7932809
## 91 92 93 94 95 96
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## 92 0.2980837
## 93 2.1752304 2.2484713
## 94 2.5608644 2.7092048 1.0024825
## 95 2.1995107 2.1704225 0.9816738 1.8881398
## 96 1.0002584 1.1422761 2.3088964 2.5282934 2.5772866
## 97 0.6964953 0.7323744 2.3196803 2.7278251 2.1868219 1.3252143
## 98 3.0545600 3.0694373 3.7319047 4.0943943 4.0067259 2.4888725
## 99 3.3334283 3.4667984 3.8012988 3.7835123 4.3658687 2.5661983
## 100 1.9235164 1.9985993 2.8330844 3.1360880 3.1563135 1.3242342
## 101 2.0027735 1.9815608 2.4677894 2.9781596 2.4110166 2.1216899
## 102 1.9451337 1.9531119 2.3510164 2.7814810 2.4332709 2.0074344
## 103 4.0510381 4.0263694 4.3619086 4.7417665 4.2088751 3.9954551
## 104 2.1390094 2.0723045 2.6697964 3.2461391 2.2606361 2.6821941
## 105 2.1278728 2.0451247 2.6837484 3.2677531 2.2795721 2.6478307
## 106 2.5643917 2.4846692 3.1119616 3.6916089 2.5681413 3.1570834
## 107 2.6417031 2.5926287 3.1566864 3.7097214 2.6351597 3.2344348
## 108 2.1704948 2.1227989 2.7132461 3.2591415 2.3357026 2.6923157
## 109 2.2153637 2.1050266 2.7876884 3.4621330 2.3598689 2.7084856
## 110 2.2822272 2.2159113 2.8232530 3.4439547 2.3664224 2.8281816
## 111 1.9775502 2.0751249 2.3177947 2.5741232 2.3555548 2.3245596
## 112 1.6942780 1.6440017 2.2231033 2.8471178 2.0555600 2.1429923
## 113 2.2584769 2.1816500 2.8065963 3.4141395 2.2485083 2.9748588
## 114 2.2809195 2.1999967 2.8303870 3.4907765 2.2571174 2.9869547
## 115 1.7857428 1.7016457 2.3538665 2.9450169 2.0099241 2.4470640
## 116 2.2215283 2.1647034 2.7494222 3.3265568 2.2520936 2.8588293
## 117 1.6546819 1.6571469 2.1504143 2.6344580 1.9407255 2.2524720
## 118 1.7832855 1.7063097 2.3163157 2.8516481 1.9593301 2.4477730
## 119 2.0748581 2.0911421 2.5365552 2.9689764 2.2272815 2.6264989
## 120 1.9675055 2.0031310 2.3705124 2.6979306 2.1444686 2.6081147
## 121 3.6232748 3.6393592 2.7426350 3.0849573 2.5307914 4.0451367
## 122 3.6530050 3.6278818 2.8656669 3.3631147 2.5018301 4.1121313
## 123 3.8729395 3.8381834 3.2045999 3.7611446 2.7232066 4.3693875
## 124 4.4350898 4.4104760 3.9160390 4.4836253 3.3567465 4.9970713
## 125 3.9244370 3.8780400 3.2854108 3.8512298 2.7642705 4.4555194
## 126 3.7071311 3.6742996 2.9667846 3.4836664 2.5647489 4.1719819
## 127 4.6814713 4.6625545 4.2043325 4.7279761 3.6386697 5.2641765
## 128 4.0681718 4.0155501 3.6849126 4.1893110 3.1864468 4.6414418
## 129 3.8648048 3.8043399 3.4511900 4.0643757 3.0270334 4.3591160
## 130 4.1552131 4.1063872 3.7747927 4.2741486 3.2630031 4.7581423
## 131 3.7563327 3.6873545 3.3055877 3.9108165 2.9211784 4.2050841
## 132 3.7287908 3.6612502 3.2625373 3.8428156 2.8767848 4.1790941
## 133 3.6935440 3.6284906 3.2130831 3.7748919 2.8774215 4.0626782
## 134 3.8693960 3.8138779 3.4240475 3.9377458 2.9628393 4.3825959
## 135 4.2961091 4.2454814 3.9376782 4.4459844 3.4661256 4.7301140
## 136 3.8977015 3.8438646 3.4814612 4.0887231 3.0327026 4.4013523
## 137 3.9283702 3.8836465 3.5076859 4.0342804 3.0538910 4.4527959
## 138 3.8466342 3.7829754 3.4254778 4.0402141 3.0095620 4.3427739
## 139 4.3126928 4.2657091 3.9796423 4.5342923 3.4431105 4.9263515
## 140 4.0119402 3.9631677 3.6313274 4.2097062 3.1570396 4.5487494
## 141 4.3795583 4.3546116 4.0405842 4.6089217 3.5545345 4.9607430
## 142 5.6411782 5.6277084 5.4391975 5.8805226 4.8625312 6.2668312
## 143 6.8164989 6.7923559 6.8665947 7.2093657 6.4943006 7.4323801
## 144 5.4782612 5.4504821 5.5354485 5.9487226 5.0870074 6.1950489
## 145 5.9599975 5.9370281 6.0213140 6.3831123 5.5408355 6.7154880
## 146 5.9407660 5.9246990 6.0044516 6.4563401 5.6284898 6.4521207
## 147 5.5038589 5.4623584 5.5483556 5.9164436 5.2136951 5.9844878
## 148 5.8883291 5.8727092 5.9412528 6.2894997 5.4791539 6.6150556
## 149 5.6355359 5.6261414 5.6790208 6.0328282 5.2533361 6.3046177
## 150 5.1201374 5.0903535 5.1524110 5.5443507 4.7618916 5.7953691
## 151 4.6640085 4.6185212 4.6731326 5.0793286 4.3884193 5.2373186
## 152 4.9076776 4.8516645 4.9344678 5.2771425 4.5863362 5.5103179
## 153 6.4001897 6.3673854 6.3939124 6.5871470 6.1526709 6.9153623
## 154 5.0212369 4.9793635 5.0507108 5.4247773 4.7233611 5.5481547
## 155 6.1808506 6.1468821 6.1891389 6.5199780 5.9576265 6.6408971
## 156 6.9434069 6.9362714 6.9321862 7.1820893 6.7898159 7.2164454
## 157 6.0432716 6.0121352 6.0714355 6.3628552 5.7702279 6.4664033
## 158 4.0100478 3.9689525 3.8277304 4.2047431 3.8341687 3.9597873
## 159 3.4344137 3.3435716 3.2775183 3.7549595 2.9752160 3.8234282
## 160 4.6090854 4.5447661 4.5998258 5.0051284 4.4119090 5.0733072
## 161 5.1937443 5.1511994 5.0622579 5.3380162 4.9564085 5.3767153
## 162 4.7596645 4.7470448 4.5602222 4.8238318 4.7338717 4.5047606
## 163 6.3353141 6.3154884 6.2012682 6.4570571 6.3125509 6.1476155
## 164 6.5790765 6.5711319 6.4354579 6.7103246 6.5865652 6.3605002
## 165 3.3391315 3.2823537 3.1311011 3.5940118 2.7661077 3.8544121
## 166 3.6857673 3.6382995 3.5113995 3.9426119 3.2657903 3.9230500
## 167 4.9873189 4.9716584 4.8140165 5.1526113 4.9624545 4.7290819
## 168 3.7124602 3.7064994 3.4862735 3.8130981 3.2956984 3.9651976
## 169 3.4641331 3.4054523 3.2971353 3.8239552 2.9955556 3.8029658
## 170 3.3525909 3.2911553 3.1663535 3.7255621 2.8518463 3.7521082
## 171 3.6365087 3.5804032 3.4845096 3.9947324 3.0546535 4.1343231
## 172 3.4531451 3.3786020 3.2901537 3.8116866 2.8550967 3.9838818
## 173 1.8193857 1.7501756 2.9856503 3.4306940 2.5441883 2.5086827
## 174 0.9794205 0.8439498 2.4858148 3.0156027 2.2866228 1.6035822
## 175 1.0856165 1.0993566 2.4451260 2.7400902 2.3247547 1.7597601
## 176 1.6383096 1.8554007 2.4542618 2.3042849 2.9845468 1.3722431
## 177 1.1606736 1.3520857 2.2890194 2.3633564 2.4667630 1.5753744
## 178 0.8742291 0.8194090 2.3250781 2.7016552 2.3126408 1.3214565
## 179 1.2972979 1.2994593 2.5271553 2.9390889 2.6298401 1.2612393
## 180 1.9429630 2.0391875 2.9129086 3.0567148 3.2614686 1.3819739
## 181 2.8022606 2.8073801 3.6521496 4.0678942 3.8097754 2.3894514
## 182 1.6321174 1.7386288 2.7852496 2.9081879 2.9238315 1.4612795
## 183 2.3062692 2.2473731 3.3319754 3.7657523 3.3802982 1.9748647
## 184 1.6582355 1.5260738 2.9530703 3.4337195 2.8293426 1.6464002
## 185 1.7281342 1.6574536 3.0156041 3.4415275 2.6189131 2.2582342
## 186 1.1624154 1.2565406 2.5736611 2.8909090 2.5170757 1.4027642
## 187 3.7066738 3.7983412 4.2441733 4.3231113 4.6776534 3.0247069
## 188 2.8920554 3.0074398 2.7224518 2.7186257 3.1667490 2.6035735
## 189 3.0490706 3.1819157 2.7850683 2.5935985 3.3195751 2.7460100
## 190 3.2713071 3.3844379 3.0630297 3.0590373 3.5696720 2.8472524
## 191 3.8058778 3.9494580 3.4836627 3.2691442 4.0680120 3.3022390
## 192 3.3917735 3.5097370 3.0818354 2.9526417 3.5872775 3.0418934
## 193 3.8426508 3.9660983 3.5333168 3.3767747 4.1184439 3.3307388
## 194 3.9837438 4.1369308 3.4617768 3.1548981 4.0798659 3.5956545
## 195 3.7762332 3.9090563 3.2685188 3.0131413 3.8235721 3.4281910
## 196 5.6217804 5.7169975 5.2491447 5.1778961 5.7396913 5.0748611
## 197 5.1867393 5.2631640 4.7449280 4.7186164 5.1324891 4.8706942
## 198 5.0217813 5.1028194 4.5927290 4.6195746 4.9046314 4.7633368
## 199 5.1518280 5.2285174 4.7271516 4.7410801 5.0737960 4.8435528
## 97 98 99 100 101 102
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## 97
## 98 3.4566989
## 99 3.7453129 1.5401119
## 100 2.3266353 1.2362434 1.6192694
## 101 2.1984578 3.0372468 3.4795956 2.3398246
## 102 2.2064401 2.9833996 3.3266190 2.2374529 0.4154576
## 103 4.0576614 5.2561221 5.6186495 4.6862626 3.7156696 3.7559685
## 104 2.0258014 4.1723934 4.6396282 3.3128630 1.3743744 1.5613327
## 105 2.0616624 4.0799921 4.5743455 3.2512492 1.2675374 1.4692751
## 106 2.3545150 4.6554197 5.1450039 3.8196888 1.9348090 2.1888248
## 107 2.3952126 4.7613054 5.1995794 3.9004954 2.0720224 2.3208148
## 108 2.0790948 4.1809640 4.6096241 3.3223023 1.3752036 1.5771084
## 109 2.2088790 3.8590925 4.4964460 3.1363373 1.1790274 1.4202253
## 110 2.1499059 4.2081310 4.7256562 3.3906722 1.4798433 1.7190146
## 111 1.9725187 4.0221276 4.0981812 3.0197317 1.4294049 1.3738405
## 112 1.9824742 3.2427622 3.7602988 2.4744416 1.5880288 1.6361430
## 113 2.1401475 4.5282001 5.0068794 3.6586015 2.3745827 2.5586661
## 114 2.1722516 4.4164534 4.9530229 3.5865526 2.3335145 2.5336529
## 115 1.9173497 3.9531736 4.4230968 3.0858244 1.9401525 2.0027732
## 116 2.1161041 4.5279044 4.9624613 3.6376099 2.3943876 2.5493575
## 117 1.7554476 3.8934429 4.1928171 2.9455439 1.8794482 1.9229293
## 118 1.8406069 4.1023041 4.5042925 3.1867540 2.0229455 2.0840465
## 119 2.0046773 4.4450747 4.6976484 3.4827589 2.3390847 2.4383384
## 120 1.8989784 4.5228233 4.6876934 3.4897400 2.3804116 2.4151087
## 121 3.6904310 5.3323579 5.4980387 4.5792415 3.3417463 3.3963273
## 122 3.7172514 5.2959197 5.6205614 4.6058717 3.3032723 3.3941098
## 123 3.8747602 5.5112247 5.9000657 4.8444624 3.4910702 3.6408992
## 124 4.3280473 6.1843727 6.5992241 5.4960619 4.1259209 4.3183459
## 125 3.9123590 5.6434615 6.0569451 4.9630511 3.5754955 3.7245155
## 126 3.7649772 5.3071163 5.6570845 4.6403588 3.3179238 3.4326680
## 127 4.5325657 6.5683177 6.9493527 5.8361865 4.4434278 4.6357148
## 128 4.0226644 5.9241793 6.3308873 5.2044473 3.1812565 3.3422109
## 129 3.9406558 5.2396079 5.7619652 4.6760662 2.7050894 2.8607866
## 130 4.0801812 6.0916514 6.4938560 5.3451505 3.3416910 3.4968249
## 131 3.8709279 5.0428088 5.5675448 4.5043970 2.5348914 2.6673929
## 132 3.8299679 5.0884237 5.5815531 4.5212007 2.5312098 2.6608878
## 133 3.8278090 4.8806958 5.3573091 4.3621927 2.3938644 2.5298130
## 134 3.8593446 5.5966445 6.0046132 4.9079074 2.8804319 3.0308507
## 135 4.2415266 6.0669512 6.4857592 5.3817309 3.4766095 3.6297879
## 136 3.9348301 5.3440988 5.8460138 4.7527359 2.7763703 2.9467005
## 137 3.9206247 5.6433980 6.0558651 4.9588822 2.9459257 3.1023643
## 138 3.9322548 5.2310680 5.7602729 4.6656741 2.7005200 2.8405563
## 139 4.2320361 6.1533340 6.6093581 5.4465458 3.4795632 3.6590085
## 140 4.0153420 5.5825246 6.0532190 4.9539056 2.9644865 3.1476581
## 141 4.3134831 6.0579443 6.5090932 5.3900326 3.5065559 3.6908002
## 142 5.3877026 7.6568163 7.9987832 6.8848446 5.0833797 5.3176111
## 143 6.8515755 8.4773094 8.8055491 7.8814109 6.9594126 7.0884981
## 144 5.5355172 7.3517919 7.7144553 6.6926018 5.6270615 5.7866295
## 145 5.9339716 8.0854426 8.4011998 7.3367495 6.1908104 6.3507070
## 146 6.0332036 7.4892991 7.8924100 6.9454532 6.0360363 6.1809826
## 147 5.6588485 7.1929944 7.5454088 6.6076069 5.6691154 5.7700826
## 148 5.8685740 7.9615956 8.2506049 7.2232063 6.1001432 6.2646416
## 149 5.6574593 7.5744084 7.8541416 6.8769543 5.8075644 5.9716537
## 150 5.2430640 6.9806828 7.3268143 6.3243578 5.2984707 5.4234544
## 151 4.9432058 6.0833355 6.4669509 5.5774290 4.7265437 4.8217123
## 152 5.1024351 6.6852822 7.0166080 6.0665190 5.0730647 5.1735948
## 153 6.5272618 8.1189048 8.3286871 7.4907077 6.6371660 6.6876545
## 154 5.2173845 6.6654971 7.0108255 6.0888641 5.1524582 5.2594053
## 155 6.3755188 7.4414281 7.7842283 6.9846308 6.2749476 6.3421480
## 156 7.1235315 8.1448776 8.3808845 7.6929955 7.0797797 7.1192158
## 157 6.1538870 7.8365081 8.1164874 7.2042223 6.2774023 6.3578819
## 158 4.3956552 3.8477636 4.2217873 3.7939612 3.8521006 3.9214363
## 159 3.6697330 4.8125188 5.2572820 4.2619517 3.6712888 3.7411501
## 160 4.9991098 5.6498540 6.0828133 5.2815590 4.6074324 4.6571568
## 161 5.3908929 6.0089597 6.2992425 5.6364300 5.3300604 5.3598449
## 162 5.1990353 3.7459469 3.9796982 4.0242177 4.4747122 4.5059383
## 163 6.6886120 5.4072025 5.6663236 5.6978955 6.0703318 6.1015941
## 164 6.9536117 5.3750237 5.6522369 5.7774763 6.2779312 6.2980939
## 165 3.4633038 5.0515779 5.4158997 4.3669999 3.6758492 3.7665756
## 166 3.8640500 5.0263358 5.3849153 4.4668557 3.9302218 4.0073280
## 167 5.4261803 3.6766592 4.0430652 4.1080222 4.6331934 4.6799520
## 168 3.8379228 5.3078504 5.5236283 4.6325606 4.0645417 4.1243079
## 169 3.6633826 4.7752014 5.2234215 4.2327932 3.6781565 3.7703227
## 170 3.5583635 4.6960348 5.1713089 4.1404952 3.5869705 3.6718810
## 171 3.6920303 5.4791474 5.8955078 4.7767060 4.0095775 4.1101619
## 172 3.5508003 5.2422618 5.6806568 4.5597602 3.8070942 3.9032074
## 173 1.5786668 4.3513699 4.7080088 3.3823650 2.8695489 3.0182666
## 174 1.2705580 3.1349188 3.6431445 2.2181646 2.2499017 2.2978300
## 175 1.1394334 3.8263673 4.0172035 2.7493052 2.5745157 2.5786953
## 176 2.0898505 2.9994192 2.5967079 1.9332453 2.8086762 2.6148271
## 177 1.2798117 3.7377555 3.6670973 2.5735611 2.7173002 2.6305198
## 178 1.2606625 3.0947134 3.4168067 2.0932105 2.3263309 2.2870827
## 179 1.7945841 2.2355073 2.6676767 1.3849065 2.2198422 2.1983476
## 180 2.3977319 1.8273823 1.7542450 1.0617676 2.5410964 2.4564480
## 181 3.2021980 1.0115621 1.9388899 1.3707315 2.8824159 2.9140831
## 182 1.8220873 2.9910608 2.9064562 2.0444661 2.4981948 2.5239906
## 183 2.6905572 1.6085735 2.3970318 1.4485880 2.5517432 2.6058295
## 184 1.9405687 2.4650611 3.1061476 1.8352505 2.2784640 2.3662851
## 185 1.4297523 4.0837622 4.4326104 3.1298949 2.7141084 2.8774630
## 186 1.1310386 3.2366431 3.3938427 2.1937039 2.3379743 2.4109558
## 187 4.1213636 1.6390795 1.1169602 2.0670586 3.7558260 3.6936086
## 188 3.1023920 3.4077490 3.1795390 2.7356739 3.7755843 3.6682579
## 189 3.2305813 3.8319741 3.4600076 3.0703414 4.0388604 3.8832509
## 190 3.5306598 3.1347243 2.8518409 2.6769628 3.9957945 3.8708514
## 191 3.9875810 3.7990788 3.2419361 3.2948897 4.5493410 4.3992131
## 192 3.5323105 3.8763019 3.5482495 3.2235998 4.2911217 4.1393646
## 193 4.0716800 3.5897987 3.1133988 3.1889151 4.5431732 4.3796990
## 194 4.1105391 4.3768518 3.8287256 3.7447917 4.9444257 4.7693688
## 195 3.8745713 4.3930519 3.9614679 3.7068411 4.7990435 4.6344146
## 196 5.8801300 4.4576055 4.0383151 4.5772958 6.1411326 6.0483954
## 197 5.3284510 5.0330318 4.8401539 4.7613985 6.1331289 6.0233913
## 198 5.0953802 5.1765971 5.0397443 4.7962241 6.0279199 5.9450656
## 199 5.2692917 4.9921161 4.8292327 4.7266548 6.0758456 5.9901485
## 103 104 105 106 107 108
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## 104 3.5889425
## 105 3.5603010 0.2489707
## 106 3.7525203 0.7340124 0.7885177
## 107 3.8344691 0.8951573 1.0136634 0.3554763
## 108 3.5436105 0.3370811 0.3423965 0.6684111 0.8103982
## 109 3.5915773 0.6298186 0.5064419 1.0758868 1.2928956 0.7214010
## 110 3.5934530 0.3613525 0.4718651 0.6235519 0.7286414 0.4027015
## 111 3.7443760 1.2059200 1.2918729 1.7008194 1.6716288 1.1622391
## 112 3.9148934 1.8218766 1.7706988 2.2420474 2.3531494 1.8461569
## 113 4.0065238 1.6020089 1.6437046 1.5134579 1.5443650 1.5962379
## 114 4.0189288 1.6127562 1.6628768 1.5567517 1.5727582 1.6245628
## 115 3.8036913 1.5869813 1.5520825 1.8710224 2.0030542 1.6075595
## 116 3.5015262 1.6611066 1.7049191 1.6407562 1.6683702 1.6394523
## 117 3.8932736 1.6150267 1.6333522 1.9244110 1.9768152 1.6214452
## 118 3.8899054 1.5791494 1.5718540 1.8420680 1.9643708 1.6331871
## 119 3.4796861 1.7658393 1.8204424 1.8385355 1.8222364 1.7057146
## 120 4.0247967 1.7893142 1.8629453 1.9449125 1.9329016 1.7827285
## 121 4.7068109 3.0559721 3.0782926 3.1200089 3.1161050 3.0196842
## 122 4.5416039 2.9689459 2.9758507 3.0049297 3.0337678 2.9481423
## 123 4.6499166 3.0462777 3.0674848 2.9618041 2.9565310 3.0127294
## 124 4.9624739 3.4615636 3.5301567 3.2161322 3.1181375 3.4116866
## 125 4.6720378 3.0575923 3.0783541 2.9505825 2.9560482 3.0318473
## 126 4.6272226 2.9849427 2.9839298 2.9796915 3.0106432 2.9538270
## 127 5.0756694 3.6797460 3.7603981 3.3747173 3.2542574 3.6203758
## 128 4.4014958 2.4059343 2.4384994 2.2194327 2.2333613 2.3802744
## 129 4.2815008 2.3087513 2.2962998 2.3387418 2.4004255 2.2948724
## 130 4.5040795 2.4861249 2.5433358 2.2826459 2.2678310 2.4756716
## 131 4.2097813 2.2764530 2.2397710 2.4000348 2.5062572 2.2888132
## 132 4.2184671 2.2371785 2.2053370 2.3538163 2.4616008 2.2568276
## 133 4.1331291 2.2968444 2.2393600 2.4478620 2.5722560 2.3028323
## 134 4.2479546 2.2518559 2.2738070 2.1919671 2.2410013 2.2637288
## 135 3.3491519 2.7808065 2.8113550 2.6491564 2.6694679 2.7529348
## 136 4.2879176 2.2984219 2.3122435 2.2847222 2.3132132 2.2903165
## 137 4.1814558 2.2959746 2.3233473 2.1983049 2.2138771 2.2685628
## 138 4.2393943 2.3066502 2.2910939 2.3675681 2.4417800 2.3031914
## 139 4.5528506 2.6285039 2.6927990 2.3821946 2.3290385 2.5967493
## 140 4.3882580 2.3709706 2.3922599 2.2482764 2.2498877 2.3302928
## 141 4.5931907 2.7619550 2.8396236 2.5520253 2.4466634 2.7088117
## 142 5.7725421 4.0922171 4.2073576 3.5886876 3.3885470 4.0179250
## 143 7.5205443 6.4228748 6.4682648 6.2216314 6.1637071 6.3920314
## 144 6.3526847 5.0129772 5.0657282 4.7669852 4.6946776 4.9715272
## 145 6.7362848 5.4124412 5.4858742 5.0933049 4.9954555 5.3712898
## 146 5.3044710 5.5590631 5.5991482 5.3930236 5.3301758 5.4919559
## 147 4.8801532 5.2457838 5.2457614 5.1439780 5.1682522 5.1974393
## 148 6.6708948 5.3650265 5.4373229 5.0492601 4.9457295 5.3170885
## 149 6.2782373 5.1737615 5.2355185 4.8958270 4.8001405 5.1151874
## 150 5.8054768 4.7636161 4.7981355 4.6011702 4.5687121 4.7266436
## 151 5.6469056 4.5293871 4.5110504 4.5183791 4.5605965 4.5037967
## 152 5.6144877 4.6799631 4.6678618 4.5828876 4.6324072 4.6549925
## 153 6.9839666 6.2336743 6.2374089 6.1603292 6.1915488 6.2202401
## 154 5.1380475 4.7990679 4.7932449 4.7143568 4.7428967 4.7564139
## 155 6.6282084 6.0463789 6.0435874 6.0355680 6.0599216 6.0300888
## 156 6.0406446 6.8804109 6.8787837 6.8955871 6.9122989 6.8361751
## 157 4.8925156 5.8003154 5.8091649 5.6955652 5.7148914 5.7530192
## 158 5.4178833 4.5077779 4.3925872 4.7196501 4.8495602 4.4613077
## 159 4.7331798 3.6364626 3.5595046 3.7322700 3.8732884 3.6240716
## 160 5.5934213 4.6573379 4.5988589 4.7755055 4.8803649 4.6518580
## 161 6.0931796 5.4226652 5.3651718 5.5322275 5.6288036 5.4057056
## 162 6.1778216 5.3921408 5.2683384 5.6695494 5.7945553 5.3417145
## 163 7.5145963 6.8177401 6.7156463 7.0525186 7.1591825 6.7847911
## 164 7.7257590 7.0907878 6.9951471 7.3598003 7.4525227 7.0586516
## 165 4.9911054 3.4343095 3.4182985 3.4675710 3.5339318 3.4359554
## 166 3.9587264 3.8749842 3.8290338 3.9569592 4.0465927 3.8396190
## 167 6.2941721 5.5819667 5.4629858 5.8649056 5.9792189 5.5342167
## 168 3.9131232 3.9013158 3.8883820 3.9611717 4.0033350 3.8534078
## 169 4.2547646 3.6226843 3.5778014 3.7083941 3.7942999 3.5941135
## 170 4.4498272 3.5153870 3.4791419 3.6239103 3.7056577 3.5044073
## 171 4.2692167 3.5893965 3.5957501 3.5712668 3.6131705 3.5790651
## 172 4.6283396 3.4598842 3.4471092 3.4725134 3.5464694 3.4658645
## 173 4.4044987 2.3474845 2.3668214 2.2737745 2.3041075 2.3342957
## 174 4.2018437 2.3298613 2.2795279 2.6175179 2.7334525 2.3491120
## 175 4.2772618 2.3806394 2.3781543 2.5990656 2.6649237 2.3814478
## 176 4.7346846 3.3547101 3.3364869 3.8172265 3.8573574 3.3365164
## 177 4.4370402 2.6984085 2.7410213 3.0389932 3.0415530 2.7152644
## 178 4.2883486 2.5270116 2.4872739 2.9067325 3.0229729 2.5760141
## 179 4.3977524 2.8463868 2.7752346 3.2500183 3.3561242 2.8480227
## 180 4.8279370 3.4541023 3.3752450 3.8822585 3.9685855 3.4205698
## 181 5.1146206 3.9103864 3.8134066 4.2920008 4.3859543 3.8824133
## 182 4.6393037 2.9578138 2.9098269 3.2014455 3.2487366 2.8908890
## 183 4.8021001 3.4539801 3.3327759 3.8036624 3.9486332 3.4413492
## 184 4.4680861 2.8199943 2.7091705 3.1125981 3.2765090 2.8323752
## 185 4.3400613 2.3360713 2.3434832 2.3018740 2.3452330 2.3304982
## 186 4.2851278 2.4548174 2.4641819 2.6757520 2.6831322 2.4321306
## 187 5.8766469 4.9284718 4.8434258 5.3516619 5.4172445 4.8827463
## 188 5.4505368 4.2828989 4.2705859 4.6640686 4.6930669 4.2841021
## 189 5.5172214 4.4739861 4.4794235 4.8909446 4.9176570 4.5002631
## 190 5.7362973 4.6741286 4.6584318 5.1117116 5.1450805 4.6938444
## 191 6.0487636 5.1820521 5.2002596 5.6409394 5.6462345 5.2311458
## 192 5.7867048 4.7637554 4.7913811 5.2226984 5.2408682 4.8421768
## 193 6.1429907 5.2426577 5.2473935 5.7333636 5.7610534 5.3033781
## 194 6.3463875 5.4151731 5.4486940 5.8612536 5.8546174 5.4658839
## 195 6.0658868 5.1946284 5.2264849 5.6270192 5.6341664 5.2553671
## 196 7.6657640 6.9795720 6.9484100 7.3804001 7.4114149 6.9887204
## 197 7.3862925 6.6185722 6.6343463 7.0166541 7.0361590 6.6914293
## 198 6.9893652 6.3835439 6.4187172 6.7366094 6.7307367 6.4512959
## 199 7.3191768 6.5457473 6.5661137 6.9175588 6.9253506 6.6131019
## 109 110 111 112 113 114
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## 110 0.6191934
## 111 1.5934552 1.3837169
## 112 1.6946109 1.8845019 1.9749290
## 113 1.7947344 1.5724363 2.1488971 1.5474892
## 114 1.7367175 1.5362576 2.1987598 1.4735112 0.3118082
## 115 1.6274852 1.6870346 1.9193785 0.8395774 0.9947311 1.0506072
## 116 1.8753851 1.6470366 2.1027220 1.5756129 0.5817520 0.6945837
## 117 1.7977305 1.7259807 1.6368780 0.8909781 1.0520214 1.1221679
## 118 1.7399392 1.7251853 1.8777091 1.0638419 0.9377574 1.0647806
## 119 2.0693769 1.8058055 1.8460360 1.5904059 0.9624578 1.1074477
## 120 2.1702576 1.9192706 1.7037917 1.6378486 1.0997958 1.2924422
## 121 3.2383420 3.1010624 3.0423352 3.1584754 2.9711355 3.0306404
## 122 3.0719683 2.9837814 3.1612048 3.0787296 2.8648354 2.8959393
## 123 3.1459360 2.9980381 3.3550861 3.2596987 2.8456989 2.8524441
## 124 3.6065246 3.3259879 3.8260237 3.8550055 3.1266235 3.1007661
## 125 3.1623556 3.0146069 3.4175332 3.3201124 2.8384938 2.8550242
## 126 3.0718349 2.9843433 3.2257679 3.1068054 2.8542763 2.8827434
## 127 3.8747584 3.5428477 4.0327622 4.1639672 3.2991257 3.2956913
## 128 2.5830856 2.3719881 2.8861750 3.1625962 2.4984994 2.5476065
## 129 2.2442091 2.2397321 2.7926785 2.7341346 2.5759553 2.5283060
## 130 2.6968537 2.4451581 2.9584215 3.2886736 2.5469169 2.5920059
## 131 2.1785614 2.2599271 2.7436465 2.6101919 2.6225886 2.5860485
## 132 2.1861139 2.2427243 2.6928255 2.6182308 2.5818427 2.5641820
## 133 2.2129796 2.3160476 2.7035459 2.5680709 2.6736650 2.6593682
## 134 2.3990704 2.2559403 2.7110753 2.9199548 2.4540862 2.4903635
## 135 2.9290893 2.7306403 3.2328129 3.4558657 2.8807971 2.9136459
## 136 2.2900533 2.2138065 2.7815647 2.8006973 2.5276858 2.4778384
## 137 2.4237320 2.2504307 2.7322103 2.9556091 2.4622541 2.4797552
## 138 2.2325821 2.2518706 2.7903853 2.7164522 2.5951902 2.5497253
## 139 2.7791452 2.5140603 3.1359899 3.3970523 2.6417447 2.6372277
## 140 2.4202092 2.2706107 2.8548350 2.9696575 2.5152169 2.4894656
## 141 2.8702793 2.5926207 3.1790302 3.4288964 2.7822234 2.7251467
## 142 4.3842483 3.9180658 4.4937157 4.9957653 3.8192754 3.8372312
## 143 6.5465132 6.3509266 6.6741437 6.1898544 5.5569128 5.5680966
## 144 5.1588339 4.9214196 5.3172742 4.6700140 3.8601690 3.8713310
## 145 5.6363696 5.3277510 5.7140914 5.2861184 4.2676332 4.3155379
## 146 5.6219239 5.4282371 5.8274656 5.1394325 4.5963668 4.5595715
## 147 5.3278611 5.2145296 5.5130357 4.7563616 4.3051677 4.3525208
## 148 5.5919774 5.2786685 5.6390702 5.2104401 4.2162872 4.2634028
## 149 5.3728742 5.0833892 5.4176895 4.9077738 4.0259291 4.0608754
## 150 4.8906480 4.7085740 5.0287484 4.2873695 3.6344098 3.6632842
## 151 4.5345622 4.5159674 4.7659687 3.6814394 3.5151134 3.5247616
## 152 4.7801683 4.6977315 4.9579640 4.0889780 3.6220436 3.7056601
## 153 6.3745174 6.2766183 6.3916690 5.8842167 5.4739235 5.5646191
## 154 4.8720706 4.7781507 5.0547659 4.1804198 3.7797674 3.8253489
## 155 6.0624748 6.0285602 6.2373265 5.4845172 5.3185109 5.3221338
## 156 6.9203289 6.8609035 6.9708689 6.3861691 6.2690026 6.2857512
## 157 5.9324622 5.7886779 6.0176004 5.4462544 4.9489155 5.0226597
## 158 4.3135681 4.5436820 4.5865126 3.1064555 3.9094328 3.8875959
## 159 3.5939604 3.7043143 3.9192457 2.5079860 2.6337155 2.7012496
## 160 4.5642665 4.6856117 4.8784057 3.5848775 3.8237240 3.8233271
## 161 5.3815607 5.4742999 5.5414937 4.6468984 4.8506509 4.8830762
## 162 5.1531017 5.4306029 5.3451584 3.9926779 5.0053988 4.9633386
## 163 6.5854357 6.8345522 6.8209865 5.7224049 6.5292876 6.4744000
## 164 6.8240598 7.0872729 7.0604736 5.9430967 6.8466071 6.7613839
## 165 3.5091698 3.4791524 3.6704081 2.4581276 2.2247090 2.2916089
## 166 3.8820197 3.9033219 4.0672046 2.8841297 2.9326999 2.9778557
## 167 5.2921454 5.5854079 5.5706806 4.1630608 5.2212657 5.1396049
## 168 4.0071856 3.9331010 3.9684025 3.0408720 2.9237758 2.9963304
## 169 3.5837167 3.6277359 3.8684236 2.4912762 2.5829439 2.5893261
## 170 3.4682242 3.5207170 3.7678633 2.3194354 2.4443666 2.4315034
## 171 3.6761624 3.5864421 3.8873110 2.8187948 2.3797163 2.4236344
## 172 3.5193033 3.4864650 3.7817122 2.5687964 2.2334085 2.2889814
## 173 2.5784790 2.3920254 2.6455605 2.2226018 1.5381480 1.6668967
## 174 2.2941043 2.4158185 2.4947900 1.4316592 1.9334996 1.9389011
## 175 2.5858157 2.5270329 2.3186762 1.8786005 1.9021652 2.0281473
## 176 3.4617449 3.5255795 2.7134952 2.4241475 3.3077963 3.3602491
## 177 2.9546345 2.8585018 2.2608142 2.1157555 2.4024547 2.4892202
## 178 2.5627172 2.6852696 2.4880902 1.6314557 2.2743578 2.3179296
## 179 2.7259939 2.9351766 2.7536405 1.6592513 2.7016160 2.6693399
## 180 3.3620317 3.5621637 3.0996093 2.7189206 3.7294976 3.7197918
## 181 3.6133280 3.9109363 3.8413073 3.0638360 4.1688072 4.0629747
## 182 3.0584748 3.0662225 2.6604203 2.6210358 3.0638253 3.1245290
## 183 3.1940305 3.5076008 3.5129162 2.7183059 3.6891106 3.6357629
## 184 2.6590676 2.9100926 3.0171284 2.3252633 2.9855961 2.9789672
## 185 2.5492652 2.3917257 2.6142092 2.5785379 2.1630232 2.2496071
## 186 2.6065521 2.5231928 2.3064224 2.2932606 2.4926417 2.5183721
## 187 4.7420859 4.9820117 4.5407846 4.0694865 5.2329065 5.1714898
## 188 4.3207481 4.3918955 3.8627587 3.2608875 4.0322431 4.0357987
## 189 4.5797739 4.6252493 3.9637659 3.5476406 4.2692277 4.3010823
## 190 4.6563560 4.7776214 4.2354421 3.5732440 4.5233168 4.4935917
## 191 5.2575599 5.3137928 4.6225180 4.2300904 5.0858747 5.0728304
## 192 4.8578943 4.9116790 4.2891006 3.8532861 4.6206696 4.6158788
## 193 5.2677016 5.3789839 4.7269986 4.2217898 5.1837213 5.1587897
## 194 5.5347044 5.5575629 4.8220181 4.7200291 5.4327146 5.4377131
## 195 5.3234939 5.3460103 4.6687948 4.5403026 5.1886321 5.2045881
## 196 6.9009969 7.0531520 6.5680134 6.0059462 6.9543163 6.9038661
## 197 6.6276096 6.7166766 6.2819757 5.6170095 6.3460118 6.3056321
## 198 6.4269046 6.4575605 6.0742326 5.4585253 6.0411313 5.9963011
## 199 6.5561789 6.6259110 6.2310812 5.5591775 6.2436394 6.1945704
## 115 116 117 118 119 120
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## 116 1.0143920
## 117 0.6114966 1.0504785
## 118 0.4216386 0.9821804 0.5332130
## 119 1.1316964 0.5950068 0.8863748 1.0349129
## 120 1.1273699 1.0625079 0.7483175 0.8766647 0.7398350
## 121 2.9935444 2.9722020 2.8839318 2.9465858 2.8866347 2.8584412
## 122 2.9013190 2.8669810 2.8950337 2.8948491 2.8919672 2.9440404
## 123 3.0635014 2.8800614 3.0621972 3.0634281 2.9684544 3.0875683
## 124 3.5982118 3.1678520 3.5782469 3.6060230 3.3086655 3.4986110
## 125 3.0705573 2.8786074 3.1026159 3.0666461 2.9961320 3.1039731
## 126 2.9339928 2.8865343 2.9368273 2.9310817 2.9329054 2.9966448
## 127 3.8395823 3.3214856 3.8104957 3.8285311 3.4537474 3.6474983
## 128 2.7888950 2.5712492 2.8541128 2.7659557 2.7223303 2.7817723
## 129 2.6128971 2.6530139 2.7382652 2.7120769 2.8288902 2.9437892
## 130 2.8866147 2.6246240 2.9407605 2.8523706 2.7829388 2.8211032
## 131 2.5344394 2.6847543 2.6720366 2.6222023 2.8416450 2.9289887
## 132 2.5104494 2.6461369 2.6273377 2.5652110 2.7876670 2.8494593
## 133 2.5452961 2.7144971 2.6369534 2.5963070 2.8198448 2.9110572
## 134 2.6303793 2.5078692 2.6762607 2.5914268 2.6351067 2.6828275
## 135 3.1068997 2.6656553 3.1883193 3.1083082 2.8009540 3.1336068
## 136 2.6580632 2.6034411 2.7427409 2.7285479 2.7769411 2.8998551
## 137 2.6700864 2.4940835 2.7241048 2.6804747 2.6259136 2.7348299
## 138 2.5877491 2.6591927 2.7322582 2.6926752 2.8378520 2.9452060
## 139 3.0402446 2.7216670 3.1114533 3.0623934 2.9216633 3.0375316
## 140 2.7515028 2.6065763 2.8246559 2.8078671 2.7782393 2.9032561
## 141 3.1787150 2.8476637 3.2095603 3.2470294 3.0228390 3.1920309
## 142 4.5836418 3.9242495 4.5159399 4.5236798 4.0697420 4.2082763
## 143 5.9197940 5.6148613 5.9255420 5.9040605 5.7195315 5.7916821
## 144 4.3479392 3.9443402 4.3426553 4.3267749 4.0796880 4.1868095
## 145 4.8546662 4.3460952 4.8327703 4.7892226 4.4714764 4.5410526
## 146 4.9175320 4.3656211 4.9615808 4.9970237 4.4794949 4.9213211
## 147 4.4470644 4.0340165 4.5405283 4.4697608 4.1110020 4.4808651
## 148 4.8089351 4.2891124 4.7588118 4.7376012 4.3912234 4.4745901
## 149 4.5669045 4.0478872 4.5052800 4.5151017 4.1265132 4.2789387
## 150 3.9669608 3.6280330 3.9910236 3.9580175 3.7346115 3.8748103
## 151 3.5538652 3.5351189 3.6172077 3.5876114 3.6203347 3.7276823
## 152 3.7680301 3.5952540 3.8363128 3.7212770 3.6756496 3.7730767
## 153 5.5706077 5.4406227 5.6047825 5.5064523 5.4622697 5.4665754
## 154 3.9190763 3.6249254 3.9833811 3.9258201 3.6966831 3.9635552
## 155 5.3525217 5.2676958 5.4147699 5.3865553 5.3357573 5.4617628
## 156 6.2414972 5.9819168 6.2920658 6.2956285 5.9765141 6.3037834
## 157 5.0842969 4.6003194 5.1607338 5.0787271 4.6340309 5.0223341
## 158 3.5235315 3.9137530 3.5235836 3.6060586 3.8694207 4.0220401
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## 160 3.5929026 3.8163144 3.7211120 3.6656373 3.8934468 3.9869599
## 161 4.6450543 4.8066952 4.7027657 4.6674191 4.8069424 4.8817365
## 162 4.5521843 5.0155613 4.5045924 4.6478680 4.9217510 5.0483294
## 163 6.1723951 6.5562104 6.1596766 6.2664707 6.5138671 6.6204484
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## 165 2.2346353 2.2890013 2.2542220 2.1716391 2.3474853 2.3479139
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## 168 2.8558389 2.5881906 2.8213148 2.8398859 2.4889708 2.8542399
## 169 2.4276624 2.4138975 2.5288145 2.5015766 2.4817361 2.7907283
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## 175 1.6450959 1.8878511 1.4786455 1.5070541 1.7097330 1.5218046
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## 177 2.0767917 2.3293544 1.7202371 1.9357283 1.9934924 1.7232616
## 178 1.7383673 2.2603223 1.6528722 1.6863632 2.1447248 2.0147582
## 179 2.1384277 2.6936027 2.0488321 2.2190760 2.5788791 2.5939645
## 180 3.2090283 3.7140032 3.0251590 3.2522881 3.4963055 3.4715017
## 181 3.7164326 4.1922285 3.6532373 3.8634283 4.1279844 4.2523063
## 182 2.8272158 3.0732729 2.5559980 2.7554552 2.8194197 2.7716931
## 183 3.2317520 3.7231534 3.2172879 3.3233753 3.6849316 3.7728553
## 184 2.6091154 3.0364276 2.6238013 2.6308109 3.0358774 3.0768389
## 185 2.3662144 2.2295346 2.2471499 2.2160206 2.2246046 2.2376347
## 186 2.3991953 2.4869639 2.1329666 2.3204021 2.3038707 2.3019640
## 187 4.7390186 5.2182988 4.5370051 4.8197867 5.0017666 5.0531737
## 188 3.5933745 3.9791990 3.3497194 3.5808534 3.7192162 3.6188572
## 189 3.8014976 4.1759178 3.5287923 3.7372008 3.8708369 3.7035179
## 190 4.0343988 4.4714917 3.7911484 4.0405442 4.2232869 4.1394588
## 191 4.6505510 4.9901919 4.3165529 4.5774045 4.6773462 4.5531585
## 192 4.1819137 4.5354263 3.8895269 4.0913774 4.2645736 4.0932441
## 193 4.6835184 5.1046431 4.3951316 4.6339065 4.8251801 4.6935469
## 194 5.0183804 5.3434277 4.7136265 4.9449886 5.0367185 4.8559658
## 195 4.7824689 5.0834985 4.5048298 4.6951111 4.7976300 4.6270117
## 196 6.5328018 6.9154091 6.3045187 6.5460386 6.6903249 6.6661921
## 197 5.9711073 6.2900633 5.7653309 5.9323028 6.1064353 6.0057973
## 198 5.7549713 5.9465929 5.5387001 5.7125514 5.7701080 5.7268850
## 199 5.9204306 6.1911585 5.7026399 5.8816849 6.0148521 5.9417663
## 121 122 123 124 125 126
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## 122 0.5908187
## 123 0.9962197 0.6061508
## 124 1.9123389 1.6779101 1.1285711
## 125 1.0994216 0.6741347 0.2499356 1.1146831
## 126 0.7033016 0.2450637 0.4848935 1.5988016 0.5714966
## 127 2.2074133 2.0300978 1.5172362 0.4926439 1.4690220 1.9655875
## 128 2.2706402 2.1019826 2.0113509 2.2520183 1.9488609 2.0754870
## 129 2.3628594 2.1029401 2.0896126 2.5203438 2.0954020 2.0784646
## 130 2.3572883 2.2007918 2.0838483 2.2129791 2.0076523 2.1852861
## 131 2.3568195 2.1014397 2.1846966 2.7738877 2.1970435 2.0913957
## 132 2.2814239 2.0507502 2.1494002 2.7640013 2.1575931 2.0425966
## 133 2.3138108 2.1036263 2.2349504 2.9338935 2.2739198 2.0869122
## 134 2.1507251 1.9821682 1.9813936 2.4187798 1.9519993 1.9726809
## 135 2.6950232 2.4574057 2.3769552 2.5280446 2.3332112 2.4894841
## 136 2.3239484 2.0799137 2.0139227 2.3597750 2.0222961 2.0538225
## 137 2.1793973 1.9954345 1.9375457 2.2524000 1.9138068 1.9829397
## 138 2.3814372 2.1134048 2.1318335 2.5899759 2.1294551 2.1021062
## 139 2.5615822 2.3561441 2.1385141 2.0512121 2.0736305 2.3250541
## 140 2.3244751 2.1040980 1.9737116 2.2013756 1.9652427 2.0592665
## 141 2.6932489 2.5030441 2.2429957 2.0140556 2.2277772 2.4730603
## 142 3.8716239 3.8041154 3.3779064 2.6276762 3.3255446 3.7290654
## 143 5.8553953 5.7866851 5.6195158 5.4201020 5.5862871 5.7549801
## 144 4.2577357 4.1692152 3.9418238 3.6949381 3.9081090 4.1205212
## 145 4.6586149 4.6043716 4.3485367 3.9591828 4.2846207 4.5623124
## 146 4.9387398 4.7541732 4.5505446 4.2599990 4.5474350 4.7607367
## 147 4.5573645 4.3902582 4.3462134 4.4185039 4.3149176 4.4165077
## 148 4.5771944 4.5403131 4.2817548 3.9076948 4.2339493 4.4940289
## 149 4.3521170 4.3084428 4.0662837 3.7600972 4.0438987 4.2654652
## 150 3.9694906 3.8701165 3.7409277 3.6857840 3.7083816 3.8526500
## 151 3.7650442 3.6470438 3.6585692 3.9797685 3.6661769 3.6262493
## 152 3.8744744 3.7765495 3.7802230 4.0555211 3.7428088 3.7615442
## 153 5.5972693 5.5728754 5.6098818 5.7970023 5.5640245 5.5840503
## 154 4.0288981 3.8929349 3.8625158 4.0400874 3.8473349 3.8953910
## 155 5.5116715 5.4066087 5.4067075 5.5655001 5.3994458 5.4124222
## 156 6.3552365 6.2464139 6.2740294 6.3827169 6.2773184 6.2985115
## 157 5.1345427 4.9960982 4.9750780 5.0119112 4.9326889 5.0466709
## 158 4.0512069 3.9784620 4.1639828 4.9424920 4.2830134 3.9323934
## 159 3.0765729 2.9252556 3.1093994 3.8086899 3.1151161 2.9170412
## 160 4.0049865 3.8578755 3.9922490 4.5417248 4.0113829 3.8542790
## 161 5.0364481 4.9690516 5.1111122 5.6185400 5.1357809 4.9716262
## 162 5.0046286 4.9776487 5.1867244 5.9846140 5.3336348 4.9342569
## 163 6.5688772 6.5181571 6.6690414 7.3090823 6.7876261 6.4786921
## 164 6.8808999 6.8215726 6.9659391 7.5732777 7.0968955 6.7892416
## 165 2.7469022 2.6717246 2.7717725 3.3142050 2.7796365 2.6610487
## 166 3.2838165 3.1389478 3.2671245 3.8052101 3.3016939 3.1683895
## 167 5.2712276 5.2035542 5.3740079 6.1107456 5.5284202 5.1568558
## 168 3.1827690 3.1229863 3.2437465 3.6862016 3.2815475 3.1768364
## 169 3.0541970 2.8766904 2.9785164 3.5162425 3.0155671 2.8864345
## 170 2.9623750 2.7832166 2.8908758 3.4333481 2.9243498 2.7944783
## 171 2.9807233 2.8069600 2.8285736 3.1420419 2.8086208 2.8383833
## 172 2.8538870 2.6925425 2.7642058 3.2279179 2.7435085 2.7018558
## 173 3.5814544 3.5679615 3.5873589 3.9035714 3.5926741 3.5541680
## 174 3.6936832 3.6392339 3.7998567 4.3483580 3.8385504 3.6563597
## 175 3.5556225 3.6142389 3.7979273 4.3085564 3.8233839 3.6519375
## 176 4.1461505 4.3351727 4.6555229 5.3175475 4.7526034 4.4116105
## 177 3.6865089 3.8410733 4.0734754 4.5810437 4.1303341 3.9148465
## 178 3.7667415 3.7789891 4.0148729 4.6456516 4.0603394 3.8221118
## 179 4.0111037 4.0052211 4.2211206 4.8666676 4.3089607 4.0271307
## 180 4.4295954 4.5155049 4.7720672 5.4740004 4.8930188 4.5365476
## 181 4.9664350 4.9204728 5.0792991 5.7023547 5.2137430 4.9052779
## 182 3.9446198 4.0761538 4.2576993 4.8518909 4.3592899 4.0760969
## 183 4.6101290 4.5513012 4.7327612 5.4239970 4.8373612 4.5310213
## 184 4.1393655 4.0732243 4.2433820 4.9085345 4.3110304 4.0568098
## 185 3.6675431 3.6625198 3.6926968 4.0592022 3.7167547 3.6441648
## 186 3.6819142 3.7559975 3.8743424 4.3358554 3.9565049 3.7695559
## 187 5.6534610 5.7404763 5.9694070 6.6629525 6.1352957 5.7427317
## 188 5.1239460 5.2511669 5.4904164 6.0508650 5.5878310 5.3040437
## 189 5.2451725 5.4115295 5.6952901 6.2783355 5.7829437 5.4908799
## 190 5.4884339 5.6075879 5.8603723 6.4544541 5.9748923 5.6634569
## 191 5.8604574 6.0422620 6.3152642 6.9000105 6.4376623 6.1214616
## 192 5.5512183 5.7032724 5.9787820 6.5527063 6.0743433 5.7905838
## 193 5.9642878 6.1189398 6.4085595 7.0339769 6.5277983 6.1975394
## 194 5.9440581 6.1480175 6.4363457 6.9854667 6.5398630 6.2433817
## 195 5.7712721 5.9521362 6.2393081 6.7920496 6.3291244 6.0492921
## 196 7.5103219 7.6303876 7.8565512 8.4453194 7.9983994 7.6642622
## 197 7.1553747 7.2557396 7.4834071 7.9906218 7.5791282 7.3251226
## 198 6.9305451 7.0189407 7.2043380 7.6166435 7.2952705 7.0918347
## 199 7.0874982 7.1821075 7.3805462 7.8496223 7.4811616 7.2435136
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## 128 2.3976765
## 129 2.8246786 1.1035995
## 130 2.3204224 0.3055492 1.2811121
## 131 3.1010835 1.3195909 0.4389692 1.5252155
## 132 3.0789467 1.2229742 0.5512018 1.4319177 0.2382482
## 133 3.2687060 1.5098026 0.8583714 1.7514414 0.5009277 0.4324416
## 134 2.6345103 0.5376998 0.9358684 0.7415329 0.9954258 0.8460428
## 135 2.6093694 1.4507339 1.8137141 1.5087865 1.9236694 1.8725539
## 136 2.6469320 0.9540198 0.2982588 1.1028542 0.6473141 0.6870996
## 137 2.4558768 0.4271407 0.7847936 0.6249113 1.0079885 0.9344477
## 138 2.8940280 1.1506239 0.1570906 1.3215040 0.3828009 0.5144619
## 139 2.1527570 0.7055006 1.2752124 0.5740604 1.6376061 1.6190879
## 140 2.4392706 0.7059998 0.5919787 0.8465033 0.9671360 0.9704069
## 141 2.1410347 1.2226151 1.3724972 1.1382189 1.7896269 1.8259286
## 142 2.3642063 2.6170848 3.3677979 2.4386046 3.7313878 3.6832347
## 143 5.3788859 5.6130440 5.8614064 5.5650846 6.0090529 5.9861810
## 144 3.6587373 3.9694560 4.2764258 3.9155146 4.4625544 4.4299609
## 145 3.8073358 4.2692078 4.7780331 4.1705040 4.9949987 4.9457544
## 146 4.2171302 4.7184872 4.8218838 4.7044229 4.9906413 5.0144975
## 147 4.4207145 4.4482562 4.6275373 4.4859620 4.6732022 4.6522502
## 148 3.7673734 4.2447165 4.7402934 4.1594262 4.9515261 4.9004729
## 149 3.6652001 4.1149104 4.5209436 4.0621884 4.7127515 4.6696431
## 150 3.6986526 3.7949387 4.0365559 3.7774073 4.1634227 4.1324462
## 151 4.1584927 3.8336733 3.7684206 3.9093329 3.7686824 3.7533253
## 152 4.1362259 3.8322934 4.0469068 3.8872531 4.0510800 3.9932967
## 153 5.8110162 5.5734289 5.8404252 5.5875655 5.8466804 5.7883123
## 154 4.1081091 3.9975118 4.1286225 4.0526889 4.1577026 4.1272154
## 155 5.6624263 5.5070185 5.4901273 5.5420651 5.5082823 5.5046610
## 156 6.4130227 6.4200187 6.4322168 6.4605903 6.4419280 6.4418583
## 157 4.9510605 5.0338697 5.3135596 5.0552687 5.3523612 5.3174077
## 158 5.3037990 4.8010840 4.3120350 5.0136713 4.1065297 4.1072705
## 159 4.0670919 3.5704163 3.4293303 3.7170632 3.2895990 3.2498476
## 160 4.7978904 4.2056991 3.9333142 4.3307040 3.8236630 3.8226962
## 161 5.8216880 5.4556746 5.3023866 5.5703318 5.1930244 5.1721417
## 162 6.3721230 5.8338905 5.2350203 6.0595426 5.0049394 5.0189840
## 163 7.6534433 7.2008610 6.6505622 7.3887205 6.4695933 6.4937380
## 164 7.9349580 7.5245370 6.8856989 7.7076803 6.7166193 6.7629482
## 165 3.5358457 3.2452369 3.2581360 3.3314307 3.2005707 3.1377125
## 166 4.0049039 3.8028963 3.7081328 3.9310740 3.6104475 3.5762357
## 167 6.5136881 6.0439790 5.3563342 6.2635748 5.1466017 5.1856281
## 168 3.8275343 3.7665187 3.8042859 3.8657330 3.7483111 3.7022298
## 169 3.7615443 3.5459726 3.3568256 3.6706516 3.2794671 3.2657525
## 170 3.6984933 3.4526696 3.2269094 3.5643840 3.1542940 3.1447199
## 171 3.2792340 3.2777676 3.3597015 3.3310500 3.3648836 3.3317493
## 172 3.4191733 3.2052169 3.2366151 3.2772832 3.1981348 3.1497737
## 173 4.0365310 3.7274794 3.8784729 3.7795286 3.8732965 3.8099627
## 174 4.6053194 4.0389612 3.8144889 4.1420216 3.7120113 3.6944051
## 175 4.4921061 3.9680212 3.9803802 4.0419509 3.9015747 3.8421596
## 176 5.5715901 4.9650036 4.7277207 5.0742557 4.5759237 4.5374632
## 177 4.7691254 4.2949707 4.2677807 4.3516897 4.1829778 4.1231578
## 178 4.9030732 4.2520182 4.0558971 4.3561720 3.9077978 3.8681503
## 179 5.1760866 4.5694310 4.1763695 4.7066355 4.0218045 4.0185427
## 180 5.7925748 5.2411771 4.8309086 5.3973374 4.6543557 4.6434924
## 181 6.0721806 5.6110751 4.9898522 5.7807812 4.8317019 4.8739133
## 182 5.0934385 4.6779314 4.5364994 4.8107296 4.4202357 4.3687328
## 183 5.7727589 5.2037067 4.7056788 5.3801108 4.5181437 4.5286127
## 184 5.2135301 4.6371029 4.3126858 4.7905345 4.1426701 4.1232464
## 185 4.2146328 3.9744428 4.0806638 4.0438338 4.0472029 3.9812798
## 186 4.5549631 4.2760794 4.1777996 4.3655150 4.1114078 4.0675846
## 187 7.0250991 6.5300195 5.9508750 6.7122554 5.7589625 5.7751839
## 188 6.3010570 5.7908611 5.5178011 5.8912072 5.3843003 5.3607192
## 189 6.5076708 5.9607668 5.7577237 6.0459711 5.6072987 5.5654351
## 190 6.7391604 6.2080692 5.8340675 6.3177714 5.6751998 5.6624857
## 191 7.1614073 6.6699473 6.3795269 6.7613745 6.2077331 6.1698505
## 192 6.8009944 6.2717930 6.0288955 6.3449834 5.8609683 5.8179025
## 193 7.3188713 6.7613145 6.4083004 6.8607275 6.2174422 6.1882096
## 194 7.2169624 6.8994971 6.6766584 6.9643694 6.5297386 6.4899965
## 195 7.0132518 6.6825851 6.4971660 6.7453551 6.3458854 6.3002249
## 196 8.7502102 8.4404600 7.9938257 8.5701601 7.8201893 7.8174560
## 197 8.2435519 8.0073174 7.6998747 8.0777209 7.5480622 7.5285548
## 198 7.8355703 7.7312970 7.4806962 7.7834773 7.3638875 7.3451811
## 199 8.0979750 7.9223068 7.6205289 7.9909640 7.4831108 7.4654096
## 133 134 135 136 137 138
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## 134 1.0849535
## 135 1.9956162 1.4581945
## 136 0.9877616 0.8069578 1.6898528
## 137 1.2090887 0.4292549 1.3340522 0.6199676
## 138 0.8497642 0.9666634 1.8126184 0.4082501 0.8367711
## 139 1.9478459 1.1144320 1.5855761 1.0743265 0.8168885 1.3375176
## 140 1.2601073 0.7845964 1.6317950 0.3981698 0.4743219 0.7032961
## 141 2.1241822 1.5115093 1.8286333 1.1648188 1.1486179 1.4541666
## 142 3.9283915 3.0261448 3.0344037 3.1245854 2.8329046 3.4677096
## 143 6.1155915 5.7494361 5.8123607 5.7793889 5.6783574 5.8944534
## 144 4.5819374 4.1345888 4.2440966 4.1666255 4.0438745 4.3246318
## 145 5.1332732 4.5077600 4.5405322 4.6399227 4.4188889 4.8276184
## 146 5.0961626 4.8253653 4.1707701 4.7318298 4.6386239 4.8433513
## 147 4.6801262 4.4719829 3.8721049 4.5855386 4.3987079 4.6209187
## 148 5.0659210 4.4645342 4.5023594 4.5976495 4.3793928 4.7962887
## 149 4.7958803 4.2883148 4.2528881 4.3868571 4.1945410 4.5773679
## 150 4.2513018 3.8967488 3.9083010 3.9604064 3.8246659 4.0619741
## 151 3.7685469 3.7762836 4.0235184 3.7740646 3.7704797 3.7779558
## 152 4.0279143 3.8263889 3.9199713 4.0233957 3.8588200 4.0536809
## 153 5.8440700 5.5969951 5.6494455 5.8165718 5.6303088 5.8363554
## 154 4.1449634 3.9899775 3.7526420 4.0947624 3.9538126 4.1340121
## 155 5.5386631 5.4884381 5.4882409 5.4853256 5.4578709 5.4873181
## 156 6.4339247 6.3914243 5.8132206 6.4172695 6.3111242 6.4136434
## 157 5.3447283 5.0676410 4.2517922 5.2594868 5.0001482 5.2983146
## 158 3.8438884 4.5013989 4.9301689 4.4110389 4.5848710 4.3245548
## 159 3.1714109 3.3898878 3.7010274 3.4962781 3.4785933 3.4123639
## 160 3.7654865 4.0420816 4.3386031 4.0068006 4.0823845 3.9152518
## 161 5.0907764 5.3062664 5.5027515 5.3550995 5.3614037 5.2907574
## 162 4.7118198 5.4987339 5.9698380 5.3496482 5.5822695 5.2494877
## 163 6.2586698 6.9215757 7.3332557 6.7498833 6.9826352 6.6614380
## 164 6.5334866 7.2421996 7.6389378 6.9899194 7.2746908 6.8950145
## 165 3.1392244 3.1186133 3.5543620 3.2548752 3.1989170 3.2644021
## 166 3.4764964 3.6288315 3.4272557 3.7236518 3.6510984 3.6956497
## 167 4.8886021 5.7138674 6.1473253 5.4722343 5.7659100 5.3724419
## 168 3.6327592 3.6327771 3.3437718 3.7842370 3.6336349 3.7979737
## 169 3.1969272 3.3833538 3.4036511 3.3846043 3.3905715 3.3489810
## 170 3.1058418 3.2898038 3.4456380 3.2582156 3.3007387 3.2165409
## 171 3.3710104 3.2186422 3.0923516 3.3272298 3.2067684 3.3518951
## 172 3.1790274 3.1071195 3.2910738 3.2305216 3.1521886 3.2286259
## 173 3.8275076 3.6633595 4.0165890 3.8351847 3.7253372 3.9000497
## 174 3.6508850 3.8562182 4.2823397 3.8571382 3.9154832 3.8035096
## 175 3.8280170 3.8280648 4.2316445 3.9859045 3.9052376 3.9738165
## 176 4.4286986 4.7216740 5.1757887 4.7748239 4.7911510 4.7116755
## 177 4.1016644 4.1213280 4.5264661 4.2594617 4.1921365 4.2588974
## 178 3.8008392 4.0227186 4.4786166 4.0986560 4.1253485 4.0359717
## 179 3.8899046 4.3123947 4.7696381 4.2431828 4.3760529 4.1674253
## 180 4.4583186 4.9590541 5.4511037 4.9026350 5.0314256 4.8308734
## 181 4.6704597 5.3233519 5.7775249 5.0783408 5.3527771 4.9985241
## 182 4.2234951 4.4659401 4.9339998 4.5519697 4.5489327 4.5587486
## 183 4.3247551 4.9135176 5.3878902 4.7946096 4.9939263 4.7084118
## 184 3.9725758 4.3809083 4.8533544 4.3772807 4.4880441 4.3121996
## 185 3.9565491 3.8665935 4.2176373 4.0389024 3.9501085 4.1055313
## 186 3.9930785 4.0976645 4.4852637 4.1592057 4.1556041 4.1975886
## 187 5.5167852 6.2030877 6.6822838 6.0323102 6.2596965 5.9643261
## 188 5.2494488 5.5538731 5.9596536 5.5517170 5.6168250 5.5108404
## 189 5.4658216 5.7121444 6.0897614 5.7832196 5.7996992 5.7401774
## 190 5.5232898 5.9279621 6.3543518 5.8766220 5.9987322 5.8249461
## 191 6.0233474 6.3597950 6.7413015 6.3894121 6.4636044 6.3707648
## 192 5.7124843 5.9776548 6.3698114 6.0376009 6.0924319 6.0101562
## 193 6.0370173 6.4354971 6.8544917 6.4369017 6.5452982 6.3925131
## 194 6.3942416 6.6345445 7.0099819 6.6850417 6.7239897 6.6600078
## 195 6.2111331 6.4204579 6.7563340 6.5037152 6.5202550 6.4764282
## 196 7.6205383 8.1330087 8.5331064 8.0389255 8.2094201 7.9968172
## 197 7.4232822 7.7321669 8.0778647 7.7158720 7.8254884 7.6841472
## 198 7.2622254 7.4863162 7.7170785 7.4730537 7.5555562 7.4691115
## 199 7.3590133 7.6543501 7.9835013 7.6261656 7.7395140 7.6118421
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## 140 0.7609270
## 141 0.6299581 0.9182451
## 142 2.2003132 2.7846859 2.2037091
## 143 5.5134637 5.6652952 5.5477154 5.5414731
## 144 3.8504703 4.0200564 3.8898707 3.9350935 3.9471071
## 145 4.1175183 4.4380992 4.2073735 3.7910877 4.0208548 1.0047023
## 146 4.5324462 4.6594553 4.4343203 4.8076743 4.7566565 2.6500640
## 147 4.5093328 4.5456890 4.6163114 5.1865781 4.8920849 2.8625050
## 148 4.1110766 4.3992109 4.1857439 3.7741466 4.0206826 0.9295454
## 149 4.0090097 4.2163647 4.0480012 3.8592346 4.0164371 0.7576398
## 150 3.7696253 3.8619287 3.8482036 4.2428645 4.0595751 0.9071598
## 151 3.9695452 3.7879917 4.0559454 4.9960556 4.5423096 2.1031778
## 152 4.0260794 3.9756748 4.2366026 4.8448697 4.4697499 2.0121942
## 153 5.7277417 5.7610680 5.9256617 6.2861175 2.2804423 4.5373893
## 154 4.1096088 4.0634533 4.2269834 4.8972479 4.5528789 2.1802395
## 155 5.5607955 5.4918340 5.6131151 6.3112443 2.1694981 4.4437602
## 156 6.4643311 6.4327606 6.4805482 7.1495400 3.9742850 5.5548238
## 157 5.1067176 5.2084311 5.2411065 5.6476960 5.4101395 3.7056411
## 158 5.1455231 4.5750554 5.1813471 6.5488710 6.6887526 5.2089723
## 159 3.9079161 3.5774908 4.1063845 5.3090206 5.6156641 3.8828020
## 160 4.4377286 4.1100491 4.5424072 5.7994420 5.1735404 3.2021981
## 161 5.7048126 5.4289198 5.8188531 6.8226530 4.2898916 5.7220143
## 162 6.1805552 5.5441356 6.1626715 7.5976396 7.6206805 6.3102069
## 163 7.4660346 6.9219434 7.4296375 8.7277550 6.7141063 7.5983304
## 164 7.7414975 7.1817518 7.6452097 9.0351845 7.0771645 7.9129262
## 165 3.5107099 3.2859374 3.6870127 4.6808642 5.2055273 3.2882900
## 166 4.0655850 3.7991166 4.1843645 5.2884911 5.6782031 3.9667704
## 167 6.3290872 5.6831445 6.2538979 7.7481255 7.7630523 6.4737494
## 168 4.0033227 3.8209768 4.1094117 5.0669761 5.5696293 3.8327267
## 169 3.7654336 3.4693586 3.8523650 5.0646322 5.4735387 3.6740583
## 170 3.6532485 3.3539973 3.7318936 5.0002989 5.4050743 3.5782379
## 171 3.4191624 3.3384281 3.5560789 4.4943339 5.1094181 3.1870022
## 172 3.4214811 3.2608334 3.6022981 4.6149008 5.1448828 3.2204881
## 173 3.9288176 3.8151681 4.0854105 4.7535983 6.0191014 4.4814366
## 174 4.2744023 3.9619278 4.3602221 5.5868747 6.4705353 5.0382112
## 175 4.2420867 4.0311075 4.3842716 5.3706206 6.3657674 4.9238947
## 176 5.2754328 4.9025808 5.3044779 6.5769440 7.2641818 5.9892152
## 177 4.5519627 4.3307970 4.6314202 5.6608059 6.6086124 5.2244485
## 178 4.5512336 4.2234546 4.6655417 5.9007269 6.6987143 5.3191574
## 179 4.8358758 4.4014629 4.8557833 6.2320140 6.9523569 5.6002420
## 180 5.5484731 5.0619761 5.5434949 6.8904342 7.7579176 6.5403058
## 181 5.8228233 5.2758607 5.7274576 7.1958692 8.0045671 6.8091403
## 182 4.9937601 4.6233420 5.0516936 6.0425474 7.1969763 5.8938357
## 183 5.4924382 4.9725152 5.5033008 6.8835623 7.7305307 6.5015381
## 184 4.9460964 4.5164472 5.0381575 6.2742044 7.2663591 5.9793814
## 185 4.2037533 4.0411463 4.3507990 5.0262823 6.5210823 5.1158792
## 186 4.5035096 4.2240077 4.5424552 5.4964763 6.8163998 5.4566992
## 187 6.8125747 6.2296760 6.7131660 8.1257578 8.8067030 7.6963712
## 188 6.0420919 5.6840315 6.0357358 7.2111755 7.7865642 6.5977098
## 189 6.2413712 5.9181826 6.2698301 7.4143980 7.9567903 6.8057148
## 190 6.4581148 6.0473178 6.4191776 7.6969580 8.1836074 7.0400035
## 191 6.9427195 6.5647544 6.9156803 8.0830748 8.5728092 7.4801824
## 192 6.5390112 6.2084310 6.5520147 7.7134781 8.2285941 7.1104004
## 193 7.0406916 6.6331020 7.0165033 8.2825480 8.7021030 7.6238574
## 194 7.1466034 6.8367991 7.1324775 8.2398727 8.8480110 7.8169668
## 195 6.9409287 6.6516129 6.9584127 8.0434843 8.6691358 7.6234634
## 196 8.6875817 8.2240715 8.6053036 9.8158586 10.0213621 9.0537421
## 197 8.2154532 7.8901758 8.1882914 9.2949966 9.3495753 8.3624122
## 198 7.8939868 7.6268903 7.8507497 8.8542462 8.9984746 7.9851303
## 199 8.1118702 7.7932274 8.0692904 9.1274460 9.2268652 8.2235102
## 145 146 147 148 149 150
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## 146 3.0281227
## 147 3.2562624 1.7294894
## 148 0.3300703 2.9614561 3.1975650
## 149 0.9098961 2.4731436 2.7203874 0.6610437
## 150 1.6110869 2.2967854 2.1192402 1.5472678 1.1587445
## 151 2.9581791 3.0332704 2.4532304 2.8614218 2.4403154 1.4612094
## 152 2.5812778 3.0051865 2.0208273 2.5050664 2.1581394 1.2884282
## 153 4.6871805 5.1550253 4.5281125 4.6741373 4.5682015 4.2434123
## 154 2.7894477 2.1266080 1.1110731 2.6931483 2.1856649 1.3548345
## 155 4.8538031 4.6329339 4.3452285 4.8169592 4.5727511 4.1280117
## 156 5.8828231 4.4756990 4.1618451 5.8314100 5.4576528 5.0495955
## 157 3.8913492 2.2546613 1.0832333 3.8505683 3.4403138 3.0256117
## 158 6.0151808 5.5264541 4.8995294 5.8559450 5.3999282 4.7462343
## 159 4.5164488 4.4166268 3.5654606 4.4392924 4.0998328 3.3387122
## 160 4.0494211 3.7367174 2.9229344 3.9668703 3.5464829 2.5279447
## 161 6.2281384 6.0029730 5.3924861 6.1523007 5.8607444 5.3184461
## 162 7.1551225 6.5490299 5.9874792 6.9772535 6.4990328 5.8692720
## 163 8.3584158 7.7967203 7.3811277 8.2083541 7.7956355 7.2461816
## 164 8.7100749 7.9986705 7.7097488 8.5603024 8.1303222 7.5680004
## 165 3.8633937 4.2091431 3.5847318 3.7808566 3.5031672 2.8881674
## 166 4.5665157 3.7252631 2.9137737 4.4600692 4.0085263 3.3409081
## 167 7.3568741 6.5911496 6.1769921 7.1815574 6.6889114 6.0599900
## 168 4.3373212 3.5395605 2.7805324 4.2215211 3.7760182 3.2124292
## 169 4.3418922 3.7372460 3.1132065 4.2459482 3.8237098 3.1142761
## 170 4.2652904 3.8407217 3.2905280 4.1818361 3.7923940 3.0558087
## 171 3.6751287 3.3247002 2.7530231 3.6157140 3.2737751 2.6607586
## 172 3.7694514 3.8091802 3.1592363 3.7125782 3.4146917 2.7409667
## 173 4.8119963 5.2529538 4.8426563 4.7379110 4.5637884 4.2715481
## 174 5.5716932 5.5569524 5.0949245 5.4999544 5.2345507 4.6829787
## 175 5.3280825 5.5711011 5.0282576 5.2554005 5.0365265 4.5791777
## 176 6.5190126 6.4202066 5.8878904 6.4062961 6.0944483 5.5607777
## 177 5.6314806 5.8010451 5.3261768 5.5431821 5.3058418 4.8691051
## 178 5.8378959 5.8526302 5.2774629 5.7588244 5.4903509 4.9182419
## 179 6.2287326 5.9851083 5.5310177 6.1231881 5.7887273 5.2065914
## 180 7.1596414 6.9012683 6.4434493 7.0289821 6.6803752 6.1632660
## 181 7.5320646 7.0009908 6.7449970 7.3989251 7.0122684 6.4791013
## 182 6.3825518 6.4460333 5.9768681 6.2464331 5.9522841 5.5946875
## 183 7.1713423 6.8225219 6.3773559 7.0495688 6.6942111 6.1450867
## 184 6.5572594 6.4413129 5.9171229 6.4563525 6.1569816 5.6358860
## 185 5.4507603 5.7839876 5.3762194 5.3634990 5.1744821 4.9118546
## 186 5.9027940 5.9628425 5.6218965 5.7890052 5.5243767 5.1930612
## 187 8.4182938 7.8835009 7.5463927 8.2487982 7.8294668 7.3360835
## 188 7.1304146 6.9597117 6.5436383 7.0136465 6.7047686 6.2317411
## 189 7.2878401 7.1595791 6.6561664 7.1784785 6.8864793 6.4035222
## 190 7.6298098 7.3309211 6.9443888 7.5031235 7.1655402 6.6620390
## 191 8.0157142 7.7348246 7.3155091 7.8743129 7.5381561 7.0936696
## 192 7.6081591 7.4425730 6.9826660 7.4936769 7.1982391 6.7211548
## 193 8.1954228 7.8849395 7.4420840 8.0621956 7.7232245 7.2204012
## 194 8.2741193 8.1226834 7.7204452 8.1602872 7.8800071 7.4525482
## 195 8.0602270 7.9100947 7.4555042 7.9548488 7.6820938 7.2424488
## 196 9.6861986 9.2154095 8.8914531 9.5271912 9.1510853 8.7094554
## 197 8.8810340 8.5923737 8.2397103 8.7690553 8.4727635 8.0143963
## 198 8.4574102 8.0921137 7.8263438 8.3477172 8.0538498 7.6549209
## 199 8.7403275 8.4394939 8.1433318 8.6211665 8.3206223 7.9017682
## 151 152 153 154 155 156
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## 152 1.1075324
## 153 4.3295951 4.0300131
## 154 1.3903358 1.0404052 4.2302026
## 155 4.0111305 4.0973786 1.6981557 4.0462833
## 156 5.0976237 5.0041871 3.2765893 4.4787292 2.6126615
## 157 3.4775438 2.9043939 4.8851473 2.1194969 4.8670032 4.1650922
## 158 3.6154292 4.1473046 6.1321662 4.2127341 5.6116006 6.4368508
## 159 2.5651328 2.7135004 4.9813401 2.9256325 4.7998957 5.6617724
## 160 1.1178886 1.8408664 4.6349891 2.0334096 4.2048628 5.2158169
## 161 4.7734961 4.9126976 3.2998504 4.9894190 2.8896245 4.0437513
## 162 4.6626352 5.2806762 7.0503659 5.3160365 6.4260836 7.2001151
## 163 6.2509796 6.7972306 6.1440869 6.8177858 5.2746870 6.2784507
## 164 6.5608487 7.2044996 6.6552242 7.1626956 5.6287015 6.5604087
## 165 2.4080976 2.5372066 4.8336511 2.8472091 4.7262183 5.7721749
## 166 2.8340419 2.8751148 5.0835703 2.6180637 4.7929406 5.0335518
## 167 4.8634563 5.5740355 7.3383137 5.5334113 6.5627301 7.3108037
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## 199 8.5793615 5.9136417 6.2548396 7.1237228 7.2263842 6.0244612
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## 199 7.2864292 7.3374655 6.1867214 6.2763044 6.1148226 6.2982696
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## 199 6.1698988 6.0902608 6.4969010 6.3611408 5.7628650 5.1863285
## 175 176 177 178 179 180
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## 176 1.8731928
## 177 0.8992104 1.3246698
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## 187 4.2951084 3.1195848 4.0824551 3.6974684 2.8624186 1.8635767
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## 199 5.3103750 4.6587670 4.9546721 4.9503848 4.7873063 4.9078306
## 181 182 183 184 185 186
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## [ reached getOption("max.print") -- omitted 307 rows ]# look at the summary of the distances
summary(dist_eu)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1343 3.4625 4.8241 4.9111 6.1863 14.3970then run k-means algorithm on the dataset and investigate what is the optimal number of clusters and run the algorithm again.
km <-kmeans(Boston_scaled, centers = 3)
# plot the dataset with clusters
pairs(Boston_scaled[6:10], col = km$cluster)
set.seed(123)
# determine the number of clusters
k_max <- 10
# calculate the total within sum of squares
twcss <- sapply(1:k_max, function(k){kmeans(Boston_scaled, k)$tot.withinss})
# visualize the results
qplot(x = 1:k_max, y = twcss, geom = 'line')
# The optimal number of clusters is when the value of total WCSS changes radically. In this case, two clusters would seem optimal
km <-kmeans(Boston_scaled, centers = 2)
pairs(Boston_scaled, col = km$cluster)
Dimensionality reduction techniques
In this part we will analyse a data set named humanW, it originates from the United Nations Development Programme. See their data page for more information. For a nice overview see also the calculating the human development indices pdf. Most of the variable names in the data have been shortened and two new variables have been computed. See the meta file. For the modified data please check our renamed variables and wrangled raw data, as well as R script for data wrangling.
Now, let’s have a look on our data set, the data now have 155 observations and 8 variables.
humanW <- read.csv(file = "C:/Users/ahmed/Desktop/IODS-project/data/human.csv")
row.names(humanW) <- humanW$X
humanW <- humanW[-1]
dim(humanW)## [1] 155 8Graphical overview of the data and summaries of the variables.
library(ggplot2)
library(GGally)
library(dplyr)
library(corrplot)
p0 <- ggpairs(humanW)
p0
cor(humanW) %>% corrplot()
From the correlation matrix we can assume for example Proportion of females with at least secondary education is positively correlated with Life expectancy at birth and Expected years of schooling, whereas, it is negatively correlated with Maternal mortality ratio and Adolescent birth rate. We can see also Percetange of female representatives in parliament is very mildly correlated with Expected years of schooling. Most of the variables are normally destributed except for Maternal mortality ratio and Adolescent birth rate.
Principal component analysis (PCA) on the not standardized human data
pca_humanW1 <- prcomp(humanW)
# draw a biplot of the principal component representation and the original variables
biplot(pca_humanW1, choices = 1:2, cex = c(0.8, 1), col = c("grey40", "deeppink2"))
Principal component analysis (PCA) on the standardized human data
# standardize the variables
humanW_std <- scale(humanW)
humanW_std## popu_sec_edu_fem
## Norway 1.358818869
## Australia 1.258589759
## Switzerland 1.281222139
## Denmark 1.297388124
## Netherlands 1.045198751
## Germany 1.323253701
## Ireland 0.812408561
## United States 1.284455336
## Canada 1.442881993
## New Zealand 1.281222139
## Singapore 0.605483947
## Sweden 1.006400386
## United Kingdom 1.436415599
## Iceland 1.151894255
## Korea (Republic of) 0.699246663
## Israel 0.938503247
## Luxembourg 1.442881993
## Japan 1.022566372
## Belgium 0.715412648
## France 0.731578634
## Austria 1.442881993
## Finland 1.442881993
## Slovenia 1.307087715
## Spain 0.369460560
## Italy 0.511721232
## Czech Republic 1.439648796
## Greece 0.133437173
## Estonia 1.442881993
## Cyprus 0.666914692
## Qatar 0.366227363
## Slovakia 1.413783219
## Poland 0.776843393
## Lithuania 1.090463510
## Malta 0.427658108
## Saudi Arabia 0.165769144
## Argentina 0.029974866
## United Arab Emirates 0.573151977
## Chile 0.579618371
## Portugal -0.248080084
## Hungary 1.374984854
## Bahrain 0.042907654
## Latvia 1.407316825
## Croatia 0.957902430
## Kuwait 0.007342486
## Montenegro 0.932036853
## Belarus 1.022566372
## Russian Federation 1.106629496
## Oman -0.264246069
## Romania 0.993467598
## Uruguay -0.031455879
## Bahamas 1.158360649
## Kazakhstan 1.290921730
## Barbados 1.103396299
## Bulgaria 1.216558197
## Panama -0.044388667
## Malaysia 0.314496210
## Mauritius -0.193115733
## Trinidad and Tobago 0.139903567
## Serbia 0.097872005
## Cuba 0.611950342
## Lebanon -0.076720638
## Costa Rica -0.151084171
## Iran (Islamic Republic of) 0.220733494
## Venezuela (Bolivarian Republic of) 0.039674457
## Turkey -0.529368230
## Sri Lanka 0.560219188
## Mexico 0.010575683
## Brazil -0.024989485
## Georgia 1.109862693
## Azerbaijan 1.239190576
## Jordan 0.456756881
## The former Yugoslav Republic of Macedonia -0.490569865
## Ukraine 1.174526635
## Algeria -0.927051472
## Peru 0.029974866
## Albania 0.854440123
## Armenia 1.248890168
## Bosnia and Herzegovina -0.338609602
## Ecuador -0.493803062
## China 0.107571596
## Fiji 0.285397436
## Mongolia 0.967602021
## Thailand -0.636063734
## Libya 0.004109289
## Tunisia -0.729826450
## Colombia 0.049374048
## Jamaica 0.602250750
## Tonga 1.038732357
## Belize 0.679847480
## Dominican Republic 0.007342486
## Suriname -0.348309193
## Maldives -0.907652289
## Samoa 0.288630633
## Botswana 0.589317962
## Moldova (Republic of) 1.235957379
## Egypt -0.370941573
## Gabon -0.047621864
## Indonesia -0.500269456
## Paraguay -0.600498566
## Philippines 0.340361786
## El Salvador -0.600498566
## South Africa 0.560219188
## Viet Nam 0.130203976
## Bolivia (Plurinational State of) -0.251313281
## Kyrgyzstan 1.265056153
## Iraq -0.891486304
## Guyana 0.159302749
## Nicaragua -0.516435442
## Morocco -1.121043297
## Namibia -0.713660464
## Guatemala -1.082244932
## Tajikistan 1.284455336
## India -0.917351881
## Honduras -0.885019910
## Bhutan -0.691028085
## Syrian Arab Republic -0.836521953
## Congo -0.506735851
## Zambia -0.956150246
## Ghana -0.328910011
## Bangladesh -0.687794887
## Cambodia -1.470228583
## Kenya -0.972316231
## Nepal -1.218039210
## Pakistan -1.166308056
## Myanmar -1.049912961
## Swaziland -1.082244932
## Tanzania (United Republic of) -1.609256057
## Cameroon -1.101644115
## Zimbabwe -0.215748113
## Mauritania -1.521959736
## Papua New Guinea -1.544592116
## Yemen -1.512260145
## Lesotho -1.082244932
## Togo -1.269770363
## Haiti -1.066078947
## Rwanda -1.531659327
## Uganda -1.049912961
## Benin -1.424963823
## Sudan -1.399098247
## Senegal -1.557524904
## Afghanistan -1.599556466
## Côte d'Ivoire -1.337667502
## Malawi -1.431430217
## Ethiopia -1.538125721
## Gambia -1.227738801
## Congo (Democratic Republic of the) -1.376465867
## Liberia -1.292402743
## Mali -1.541358918
## Mozambique -1.745050335
## Sierra Leone -1.466995385
## Burkina Faso -1.761216320
## Burundi -1.618955649
## Chad -1.735350744
## Central African Republic -1.463762188
## Niger -1.712718364
## lab_force_partic_femal
## Norway 0.541064622
## Australia 0.391483737
## Switzerland 0.578459844
## Denmark 0.385251200
## Netherlands 0.372786126
## Germany 0.067391818
## Ireland 0.036229134
## United States 0.235670314
## Canada 0.565994770
## New Zealand 0.590924917
## Singapore 0.391483737
## Sweden 0.484971790
## United Kingdom 0.198275093
## Iceland 1.120690554
## Korea (Republic of) -0.150746973
## Israel 0.335390905
## Luxembourg -0.113351752
## Japan -0.231769953
## Belgium -0.312792932
## France -0.113351752
## Austria 0.129717187
## Finland 0.198275093
## Slovenia -0.013631161
## Spain -0.001166088
## Italy -0.805163347
## Czech Republic -0.088421604
## Greece -0.518466650
## Estonia 0.229437778
## Cyprus 0.216972704
## Qatar -0.107119215
## Slovakia -0.088421604
## Poland -0.225537416
## Lithuania 0.204507630
## Malta -0.911116474
## Saudi Arabia -2.014275505
## Argentina -0.312792932
## United Arab Emirates -0.375118301
## Chile -0.206839805
## Portugal 0.148414798
## Hungary -0.481071428
## Bahrain -0.830093495
## Latvia 0.148414798
## Croatia -0.487303965
## Kuwait -0.555861871
## Montenegro -0.593257093
## Belarus -0.150746973
## Russian Federation 0.285530610
## Oman -1.465812258
## Romania -0.238002490
## Uruguay 0.192042556
## Bahamas 1.045900111
## Kazakhstan 0.946179521
## Barbados 0.833993856
## Bulgaria -0.287862785
## Panama -0.219304879
## Malaysia -0.506001576
## Mauritius -0.555861871
## Trinidad and Tobago 0.029996597
## Serbia -0.499769039
## Cuba -0.568326945
## Lebanon -1.821066861
## Costa Rica -0.368885764
## Iran (Islamic Republic of) -2.238646833
## Venezuela (Bolivarian Republic of) -0.088421604
## Turkey -1.440882110
## Sri Lanka -1.085627507
## Mexico -0.462373818
## Brazil 0.428878958
## Georgia 0.248135388
## Azerbaijan 0.647017750
## Jordan -2.300972202
## The former Yugoslav Republic of Macedonia -0.587024556
## Ukraine 0.042461671
## Algeria -2.325902349
## Peru 0.977342205
## Albania -0.474838892
## Armenia 0.104787040
## Bosnia and Herzegovina -1.147952876
## Ecuador 0.135949724
## China 0.709343118
## Fiji -0.936046622
## Mongolia 0.254367925
## Thailand 0.734273266
## Libya -1.403486889
## Tunisia -1.708881197
## Colombia 0.204507630
## Jamaica 0.223205241
## Tonga 0.061159281
## Belize -0.206839805
## Dominican Republic -0.075956530
## Suriname -0.749070515
## Maldives 0.229437778
## Samoa -1.808601787
## Botswana 1.207946070
## Moldova (Republic of) -0.929814085
## Egypt -1.796136713
## Gabon 0.229437778
## Indonesia -0.069723993
## Paraguay 0.198275093
## Philippines -0.088421604
## El Salvador -0.294095322
## South Africa -0.499769039
## Viet Nam 1.276503976
## Bolivia (Plurinational State of) 0.728040729
## Kyrgyzstan 0.216972704
## Iraq -2.344599960
## Guyana -0.618187240
## Nicaragua -0.319025469
## Morocco -1.621625680
## Namibia 0.135949724
## Guatemala -0.200607268
## Tajikistan 0.397716274
## India -1.590462996
## Honduras -0.605722166
## Bhutan 0.883854152
## Syrian Arab Republic -2.431855477
## Congo 0.996039816
## Zambia 1.282736513
## Ghana 0.921249373
## Bangladesh 0.304228220
## Cambodia 1.637991116
## Kenya 0.603389991
## Nepal 1.706549022
## Pakistan -1.740043881
## Myanmar 1.413619788
## Swaziland -0.537164261
## Tanzania (United Republic of) 2.217617047
## Cameroon 0.703110582
## Zimbabwe 1.912222739
## Mauritania -1.484509869
## Papua New Guinea 1.120690554
## Yemen -1.690183586
## Lesotho 0.403948811
## Togo 1.750176780
## Haiti 0.522367012
## Rwanda 2.111663920
## Uganda 1.451015009
## Benin 0.939946984
## Sudan -1.322463909
## Senegal 0.840226393
## Afghanistan -2.288507128
## Côte d'Ivoire -0.007398624
## Malawi 1.999478256
## Ethiopia 1.600595894
## Gambia 1.226643681
## Congo (Democratic Republic of the) 1.133155627
## Liberia 0.354088515
## Mali -0.107119215
## Mozambique 2.055571088
## Sierra Leone 0.821528783
## Burkina Faso 1.532037989
## Burundi 1.918455276
## Chad 0.715575655
## Central African Republic 1.251573828
## Niger -0.780233199
## exp_year_edu life_exp_birth
## Norway 1.522355407 1.193756093
## Australia 2.472975726 1.289770723
## Switzerland 0.923816688 1.361781696
## Denmark 1.944853327 1.025730490
## Netherlands 1.663188047 1.193756093
## Germany 1.170273807 1.109743291
## Ireland 1.909645167 1.109743291
## United States 1.170273807 0.893710373
## Canada 0.959024848 1.241763408
## New Zealand 2.120894126 1.217759750
## Singapore 0.782984048 1.361781696
## Sweden 0.923816688 1.265767066
## United Kingdom 1.064649327 1.085739634
## Iceland 2.050477807 1.313774381
## Korea (Republic of) 1.311106447 1.229761579
## Israel 0.994233008 1.289770723
## Luxembourg 0.254861648 1.205757922
## Japan 0.747775888 1.421790840
## Belgium 1.099857487 1.097741463
## France 0.994233008 1.265767066
## Austria 0.888608528 1.169752435
## Finland 1.381522767 1.097741463
## Slovenia 1.275898287 1.049734147
## Spain 1.451939087 1.313774381
## Italy 0.994233008 1.373783525
## Czech Republic 1.135065647 0.833701229
## Greece 1.557563567 1.109743291
## Estonia 1.170273807 0.617668311
## Cyprus 0.290069808 1.025730490
## Qatar 0.219653488 0.785693914
## Slovakia 0.677359568 0.557659167
## Poland 0.818192208 0.689679284
## Lithuania 1.135065647 0.197604304
## Malta 0.430902448 1.073737805
## Saudi Arabia 1.099857487 0.317622591
## Argentina 1.663188047 0.557659167
## United Arab Emirates 0.043612688 0.641671969
## Chile 0.712567728 1.205757922
## Portugal 1.099857487 1.109743291
## Hungary 0.782984048 0.425639051
## Bahrain 0.430902448 0.593664654
## Latvia 0.712567728 0.305620763
## Croatia 0.571735088 0.677677455
## Kuwait 0.536526928 0.329624420
## Montenegro 0.712567728 0.545657338
## Belarus 0.888608528 -0.042432272
## Russian Federation 0.536526928 -0.186454218
## Oman 0.149237168 0.617668311
## Romania 0.360486128 0.365629907
## Uruguay 0.818192208 0.665675626
## Bahamas -0.202844431 0.449642708
## Kazakhstan 0.642151408 -0.270467019
## Barbados 0.782984048 0.473646366
## Bulgaria 0.430902448 0.305620763
## Panama 0.043612688 0.713682941
## Malaysia -0.167636271 0.365629907
## Mauritius 0.853400368 0.329624420
## Trinidad and Tobago -0.308468911 -0.150448731
## Serbia 0.430902448 0.389633564
## Cuba 0.219653488 0.929715860
## Lebanon 0.219653488 0.917714031
## Costa Rica 0.254861648 0.929715860
## Iran (Islamic Republic of) 0.677359568 0.449642708
## Venezuela (Bolivarian Republic of) 0.360486128 0.305620763
## Turkey 0.466110608 0.437640879
## Sri Lanka 0.184445328 0.389633564
## Mexico -0.026803631 0.617668311
## Brazil 0.712567728 0.341626249
## Georgia 0.219653488 0.389633564
## Azerbaijan -0.449301551 -0.102441416
## Jordan 0.114029008 0.281617105
## The former Yugoslav Republic of Macedonia 0.078820848 0.449642708
## Ukraine 0.677359568 -0.078437758
## Algeria 0.290069808 0.377631735
## Peru -0.026803631 0.353628078
## Albania -0.484509711 0.737686599
## Armenia -0.308468911 0.365629907
## Bosnia and Herzegovina 0.149237168 0.581662825
## Ecuador 0.360486128 0.509651852
## China -0.026803631 0.497650023
## Fiji 0.888608528 -0.198456046
## Mongolia 0.501318768 -0.270467019
## Thailand 0.114029008 0.329624420
## Libya 0.290069808 -0.006426786
## Tunisia 0.501318768 0.377631735
## Colombia 0.114029008 0.281617105
## Jamaica -0.273260751 0.485648194
## Tonga 0.536526928 0.137595160
## Belize 0.149237168 -0.198456046
## Dominican Republic -0.026803631 0.221607961
## Suriname -0.167636271 -0.066435930
## Maldives -0.062011791 0.617668311
## Samoa -0.097219951 0.209606132
## Botswana -0.238052591 -0.858556630
## Moldova (Republic of) -0.449301551 -0.006426786
## Egypt 0.114029008 -0.066435930
## Gabon -0.238052591 -0.870558458
## Indonesia -0.062011791 -0.330476163
## Paraguay -0.449301551 0.149596988
## Philippines -0.660550511 -0.414488964
## El Salvador -0.308468911 0.161598817
## South Africa 0.149237168 -1.710686473
## Viet Nam -0.449301551 0.497650023
## Bolivia (Plurinational State of) 0.008404529 -0.402487136
## Kyrgyzstan -0.238052591 -0.126445074
## Iraq -1.083048430 -0.270467019
## Guyana -1.012632111 -0.630521883
## Nicaragua -0.590134191 0.389633564
## Morocco -0.554926031 0.281617105
## Namibia -0.660550511 -0.822551143
## Guatemala -0.871799471 0.017576872
## Tajikistan -0.695758671 -0.270467019
## India -0.519717871 -0.438492622
## Honduras -0.730966831 0.173600646
## Bhutan -0.202844431 -0.258465190
## Syrian Arab Republic -0.308468911 -0.246463361
## Congo -0.730966831 -1.122596863
## Zambia 0.114029008 -1.386637096
## Ghana -0.590134191 -1.230613322
## Bangladesh -1.118256590 -0.006426786
## Cambodia -0.801383151 -0.390485307
## Kenya -0.766174991 -1.206609664
## Nepal -0.273260751 -0.246463361
## Pakistan -1.892836110 -0.654525540
## Myanmar -1.611170830 -0.690531027
## Swaziland -0.660550511 -2.718840091
## Tanzania (United Republic of) -1.399921870 -0.798547486
## Cameroon -0.977423951 -1.938721220
## Zimbabwe -0.801383151 -1.698684645
## Mauritania -1.646378990 -1.026582233
## Papua New Guinea -1.153464750 -1.086591376
## Yemen -1.399921870 -0.942569431
## Lesotho -0.730966831 -2.622825461
## Togo -0.343677071 -1.434644411
## Haiti -1.575962670 -1.062587719
## Rwanda -1.012632111 -0.894562116
## Uganda -1.188672910 -1.578666357
## Benin -0.730966831 -1.446646240
## Sudan -2.174501389 -0.978574917
## Senegal -1.857627950 -0.618520054
## Afghanistan -1.364713710 -1.350631610
## Côte d'Ivoire -1.505546350 -2.418794372
## Malawi -0.836591311 -1.062587719
## Ethiopia -1.646378990 -0.906563945
## Gambia -1.540754510 -1.374635267
## Congo (Democratic Republic of the) -1.188672910 -1.554662699
## Liberia -1.294297390 -1.290622466
## Mali -1.681587150 -1.638675501
## Mozambique -1.364713710 -1.986728535
## Sierra Leone -1.611170830 -2.490805344
## Burkina Faso -1.892836110 -1.554662699
## Burundi -1.083048430 -1.794699275
## Chad -2.033668750 -2.406792543
## Central African Republic -2.104085069 -2.514809002
## Niger -2.737831949 -1.230613322
## GNI MMR
## Norway 1.229380770 -0.68503778
## Australia 0.662854003 -0.67559445
## Switzerland 1.046630200 -0.67559445
## Denmark 0.735954231 -0.68031611
## Netherlands 0.754229288 -0.67559445
## Germany 0.699404117 -0.67087278
## Ireland 0.516653547 -0.66142944
## United States 1.010080086 -0.57171776
## Canada 0.644578946 -0.65198611
## New Zealand 0.333902977 -0.66615111
## Singapore 1.485231568 -0.67559445
## Sweden 0.772504345 -0.68503778
## United Kingdom 0.498378490 -0.66615111
## Iceland 0.407003205 -0.68503778
## Korea (Republic of) 0.370453091 -0.57643943
## Israel 0.297352863 -0.69448112
## Luxembourg 1.064905257 -0.65198611
## Japan 0.425278262 -0.67559445
## Belgium 0.626303889 -0.67559445
## France 0.443553319 -0.64726444
## Austria 0.681129060 -0.68503778
## Finland 0.480103433 -0.68503778
## Slovenia 0.004951951 -0.67087278
## Spain 0.315627920 -0.68503778
## Italy 0.352178034 -0.68503778
## Czech Republic -0.013323106 -0.68031611
## Greece -0.104698391 -0.68031611
## Estonia -0.086423334 -0.65198611
## Cyprus 0.041502065 -0.65670778
## Qatar -1.128101583 -0.67559445
## Slovakia -0.049873220 -0.67087278
## Poland -0.159523562 -0.68975945
## Lithuania -0.122973448 -0.65198611
## Malta 0.023227008 -0.66142944
## Saudi Arabia 0.991805029 -0.62837777
## Argentina -0.250898847 -0.37812940
## United Arab Emirates 1.211105713 -0.66615111
## Chile -0.287448961 -0.60004777
## Portugal -0.068148277 -0.66615111
## Hungary -0.177798619 -0.63782111
## Bahrain 0.461828376 -0.60004777
## Latvia -0.232623790 -0.64254277
## Croatia -0.616399987 -0.64254277
## Kuwait 1.576606853 -0.63782111
## Montenegro -0.963626070 -0.67087278
## Belarus -0.726050329 -0.69920278
## Russian Federation -0.214348733 -0.59060443
## Oman 0.388728148 -0.65198611
## Romania -0.689500215 -0.54810943
## Uruguay -0.634675044 -0.63782111
## Bahamas -0.269173904 -0.52922276
## Kazakhstan -0.323999075 -0.58116110
## Barbados -1.182926754 -0.45839775
## Bulgaria -0.890525842 -0.68031611
## Panama -0.671225158 -0.30258272
## Malaysia -0.196073676 -0.56699610
## Mauritius -0.707775272 -0.35924273
## Trinidad and Tobago -0.031598163 -0.30730439
## Serbia -1.219476868 -0.62837777
## Cuba 1.302480998 -0.32619106
## Lebanon -0.762600443 -0.62837777
## Costa Rica -1.055001355 -0.52450109
## Iran (Islamic Republic of) -0.908800899 -0.59532610
## Venezuela (Bolivarian Republic of) -0.817425614 -0.18454104
## Turkey -0.652950101 -0.60949110
## Sri Lanka 1.649707081 -0.56699610
## Mexico -0.835700671 -0.47256275
## Brazil -0.927075956 -0.37812940
## Georgia 1.265930884 -0.51033609
## Azerbaijan -0.780875500 -0.58116110
## Jordan -1.329127210 -0.46784108
## The former Yugoslav Republic of Macedonia -1.292577096 -0.67087278
## Ukraine 1.540056739 -0.59532610
## Algeria -1.109826526 -0.28369605
## Peru -1.347402267 -0.28369605
## Albania 1.704532252 -0.60476944
## Armenia 1.521781682 -0.56699610
## Bosnia and Herzegovina 1.613156967 -0.66615111
## Ecuador -1.402227438 -0.29313939
## China -1.164651697 -0.55283109
## Fiji 1.357306169 -0.42534607
## Mongolia -1.383952381 -0.38285107
## Thailand -1.073276412 -0.58116110
## Libya -0.945351013 -0.63309944
## Tunisia -1.438777552 -0.48672775
## Colombia -1.256026982 -0.31202606
## Jamaica 1.339031112 -0.32619106
## Tonga 0.790779402 -0.13732436
## Belize 1.375581226 -0.49144942
## Dominican Republic -1.274302039 -0.23175771
## Suriname -0.872250785 -0.09010769
## Maldives -1.201201811 -0.55755276
## Samoa 0.845604573 -0.43006774
## Botswana -0.744325386 0.09875900
## Moldova (Republic of) 0.827329516 -0.60476944
## Egypt -1.420502495 -0.49144942
## Gabon -0.799150557 0.42927572
## Indonesia 1.667982138 0.19319235
## Paraguay 1.393856283 -0.18454104
## Philippines 1.412131340 -0.13732436
## El Salvador 1.320756055 -0.37812940
## South Africa -1.237751925 -0.04289102
## Viet Nam 0.809054459 -0.47256275
## Bolivia (Plurinational State of) 0.973529972 0.24040903
## Kyrgyzstan 0.059777122 -0.34979940
## Iraq -1.018451241 -0.38757274
## Guyana 1.138005485 0.47649239
## Nicaragua 0.534928604 -0.23175771
## Morocco 1.174555599 -0.13732436
## Namibia 1.594881910 -0.09010769
## Guatemala 1.192830656 -0.04289102
## Tajikistan -0.470199531 -0.49617109
## India 0.900429744 0.19319235
## Honduras 0.279077806 -0.13732436
## Bhutan 1.284205941 -0.13732436
## Syrian Arab Republic -0.451924474 -0.47256275
## Congo 1.101455371 1.23195918
## Zambia 0.224252635 0.61814242
## Ghana 0.260802749 1.09030915
## Bangladesh 0.096327236 0.09875900
## Cambodia -0.378824246 0.09875900
## Kenya -0.433649417 1.18474250
## Nepal -0.561574816 0.19319235
## Pakistan 0.608028832 0.09875900
## Myanmar 0.553203661 0.24040903
## Swaziland 0.918704801 0.75979244
## Tanzania (United Republic of) -0.525024702 1.23195918
## Cameroon -0.415374360 2.08185930
## Zimbabwe -1.530152837 1.51525922
## Mauritania 0.205977578 0.80700911
## Papua New Guinea -0.488474588 0.33484237
## Yemen 0.187702521 0.57092574
## Lesotho 0.132877350 1.60969257
## Togo -1.731178464 1.42082587
## Haiti -1.511877780 1.09030915
## Rwanda -1.639803179 0.80700911
## Uganda -1.548427894 0.99587581
## Benin -1.493602723 0.90144246
## Sudan 0.242527692 0.99587581
## Senegal -0.579849873 0.80700911
## Afghanistan -1.457052609 1.18474250
## Côte d'Ivoire 0.078052179 2.69567606
## Malawi 1.448681454 1.70412591
## Ethiopia -1.676353293 1.27917585
## Gambia -1.621528122 1.32639252
## Congo (Democratic Republic of the) 1.247655827 2.74289274
## Liberia 1.558331796 2.31794267
## Mali -1.584978008 1.89299261
## Mozambique -1.767728578 1.56247589
## Sierra Leone -1.475327666 4.48990967
## Burkina Faso -1.566702951 1.18474250
## Burundi 1.466956511 2.79010941
## Chad -0.598124930 3.92330958
## Central African Republic 1.083180314 3.45114284
## Niger 1.741082366 2.27072600
## ABR parl_repres
## Norway -0.957352128 1.626810626
## Australia -0.852759925 0.834662185
## Switzerland -1.100862360 0.660563627
## Denmark -1.023026302 1.487531779
## Netherlands -0.996270157 1.391777572
## Germany -1.054647201 1.391777572
## Ireland -0.947622621 -0.088060174
## United States -0.393040707 -0.131584814
## Canada -0.794382882 0.634448843
## New Zealand -0.531686186 0.913006537
## Singapore -1.001134911 0.382005934
## Sweden -0.988973027 1.975007743
## United Kingdom -0.519524302 0.225317231
## Iceland -0.867354186 1.774794401
## Korea (Republic of) -1.093565230 -0.401437579
## Israel -0.957352128 0.138267952
## Luxembourg -0.945190244 0.643153771
## Japan -1.015729172 -0.810569191
## Belgium -0.984108273 1.870548608
## France -1.008432041 0.416825645
## Austria -1.047350070 0.817252330
## Finland -0.923298853 1.879253536
## Slovenia -1.132483259 0.590924204
## Spain -0.889245577 1.487531779
## Italy -1.049782447 0.799842474
## Czech Republic -1.027891056 -0.175109453
## Greece -0.857624679 0.007694033
## Estonia -0.738438215 -0.096765102
## Cyprus -1.013296795 -0.732224840
## Qatar -0.916001722 -1.820340830
## Slovakia -0.760329606 -0.192519309
## Poland -0.850327548 0.103448240
## Lithuania -0.889245577 0.216612303
## Malta -0.704384939 -0.688700200
## Saudi Arabia -0.898975085 -0.088060174
## Argentina 0.176135467 1.383072644
## United Arab Emirates -0.475741519 -0.296978444
## Chile 0.198026858 -0.444962219
## Portugal -0.840598041 0.904301609
## Hungary -0.852759925 -0.941143110
## Bahrain -0.811409519 -0.514601642
## Latvia -0.818706650 -0.253453805
## Croatia -0.838165664 0.425530573
## Kuwait -0.794382882 -1.689766911
## Montenegro -0.777356244 -0.314388300
## Belarus -0.646007896 0.799842474
## Russian Federation -0.521956679 -0.558126282
## Oman -0.889245577 -0.984667750
## Romania -0.393040707 -0.775749480
## Uruguay 0.270998162 -0.819274119
## Bahamas -0.453850128 -0.366617867
## Kazakhstan -0.419796852 -0.070650318
## Barbados 0.030192858 -0.114174958
## Bulgaria -0.273854244 -0.044535534
## Panama 0.762338279 -0.140289742
## Malaysia -1.008432041 -0.584241065
## Mauritius -0.395473084 -0.810569191
## Trinidad and Tobago -0.300610389 0.329776366
## Serbia -0.736005838 1.139334663
## Cuba -0.098723113 2.436368923
## Lebanon -0.855192302 -1.550488064
## Costa Rica 0.331807583 1.078400167
## Iran (Islamic Republic of) -0.378446447 -1.550488064
## Venezuela (Bolivarian Republic of) 0.876659989 -0.340503084
## Turkey -0.395473084 -0.566831210
## Sri Lanka -0.736005838 -1.315455011
## Mexico 0.395049380 1.409187428
## Brazil 0.575045264 -0.984667750
## Georgia -0.008725171 -0.836683975
## Azerbaijan -0.174126794 -0.462372075
## Jordan -0.502497664 -0.810569191
## The former Yugoslav Republic of Macedonia -0.701952563 1.078400167
## Ukraine -0.521956679 -0.793159336
## Algeria -0.903839838 0.416825645
## Peru 0.086137525 0.120858096
## Albania -0.774923867 -0.018420751
## Armenia -0.487903403 -0.888913543
## Bosnia and Herzegovina -0.779788621 -0.140289742
## Ecuador 0.725852626 1.800909184
## China -0.937893114 0.234022159
## Fiji -0.106020244 -0.601650921
## Mongolia -0.692223055 -0.523306570
## Thailand -0.149803026 -1.289340227
## Libya -1.086268099 -0.427552363
## Tunisia -1.035188186 0.904301609
## Colombia 0.519100597 -0.001010895
## Jamaica 0.558018626 -0.366617867
## Tonga -0.706817316 -1.820340830
## Belize 0.589639525 -0.662585417
## Dominican Republic 1.275569786 -0.157699597
## Suriname -0.290880881 -0.793159336
## Maldives -1.044917693 -1.306750083
## Samoa -0.458714881 -1.289340227
## Botswana -0.071966968 -0.993372678
## Moldova (Republic of) -0.434391113 -0.009715823
## Egypt -0.101155490 -1.628832416
## Gabon 1.358270598 -0.410142507
## Indonesia 0.027760481 -0.331798156
## Paraguay 0.482614945 -0.357912940
## Philippines -0.008725171 0.538694636
## El Salvador 0.701528858 0.564809420
## South Africa 0.091002278 1.722564833
## Viet Nam -0.441688244 0.294956654
## Bolivia (Plurinational State of) 0.601801409 2.688811832
## Kyrgyzstan -0.434391113 0.207907375
## Iraq 0.523965351 0.486465069
## Guyana 1.005575960 0.904301609
## Nicaragua 1.304758308 1.583285986
## Morocco -0.276286620 -0.862798759
## Namibia 0.188297351 1.461416996
## Guatemala 1.217192743 -0.662585417
## Tajikistan -0.106020244 -0.497191786
## India -0.349257925 -0.758339624
## Honduras 0.896119003 0.425530573
## Bhutan -0.152235403 -1.097831813
## Syrian Arab Republic -0.135208765 -0.740929768
## Congo 1.934743902 -0.819274119
## Zambia 1.903123004 -0.714814984
## Ghana 0.273430539 -0.871503687
## Bangladesh 0.813418192 -0.079355246
## Cambodia -0.069534591 -0.166404525
## Kenya 1.129627177 -0.009715823
## Nepal 0.645584192 0.747612906
## Pakistan -0.483038650 -0.105470030
## Myanmar -0.852759925 -1.411209218
## Swaziland 0.604233786 -0.540716426
## Tanzania (United Republic of) 1.837448830 1.313433221
## Cameroon 1.669614830 0.538694636
## Zimbabwe 0.319645699 1.235088870
## Mauritania 0.635854684 0.112153168
## Papua New Guinea 0.363428481 -1.585307776
## Yemen -0.003860417 -1.759406335
## Lesotho 1.027467351 0.512579852
## Togo 1.078547264 -0.288273516
## Haiti -0.125479258 -1.515668353
## Rwanda -0.329798910 3.184992724
## Uganda 1.932311526 1.226383942
## Benin 1.046926366 -1.089126885
## Sudan 0.896119003 0.251432015
## Senegal 1.149086192 1.896663392
## Afghanistan 0.964225554 0.582219276
## Côte d'Ivoire 2.022309468 -1.019487461
## Malawi 2.375004106 -0.366617867
## Ethiopia 0.759905902 0.399415789
## Gambia 1.669614830 -1.002077606
## Congo (Democratic Republic of the) 2.143928308 -1.106536741
## Liberia 1.708532859 -0.888913543
## Mali 3.124176164 -0.993372678
## Mozambique 2.204737729 1.626810626
## Sierra Leone 1.302325931 -0.740929768
## Burkina Faso 1.659885323 -0.662585417
## Burundi -0.410067345 1.217679014
## Chad 2.550135236 -0.523306570
## Central African Republic 1.243948888 -0.732224840
## Niger 3.834430193 -0.662585417
## attr(,"scaled:center")
## popu_sec_edu_fem lab_force_partic_femal exp_year_edu
## 55.37290 52.51871 13.17613
## life_exp_birth GNI MMR
## 71.65355 98.72903 149.08387
## ABR parl_repres
## 47.15871 20.91161
## attr(,"scaled:scale")
## popu_sec_edu_fem lab_force_partic_femal exp_year_edu
## 30.929138 16.044831 2.840251
## life_exp_birth GNI MMR
## 8.332064 54.719392 211.789590
## ABR parl_repres
## 41.112051 11.487746# summaries of the standardized variables showing means equal to zero
summary(humanW_std)## popu_sec_edu_fem lab_force_partic_femal exp_year_edu
## Min. :-1.76122 Min. :-2.43186 Min. :-2.7378
## 1st Qu.:-0.91250 1st Qu.:-0.50289 1st Qu.:-0.6782
## Median : 0.03967 Median : 0.06116 Median : 0.1140
## Mean : 0.00000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.96275 3rd Qu.: 0.58469 3rd Qu.: 0.7126
## Max. : 1.44288 Max. : 2.21762 Max. : 2.4730
## life_exp_birth GNI MMR ABR
## Min. :-2.7188 Min. :-1.767729 Min. :-0.6992 Min. :-1.1325
## 1st Qu.:-0.6425 1st Qu.:-0.826563 1st Qu.:-0.6496 1st Qu.:-0.8394
## Median : 0.3056 Median : 0.004952 Median :-0.4726 Median :-0.3298
## Mean : 0.0000 Mean : 0.000000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.6717 3rd Qu.: 0.818192 3rd Qu.: 0.1932 3rd Qu.: 0.6030
## Max. : 1.4218 Max. : 1.741082 Max. : 4.4899 Max. : 3.8344
## parl_repres
## Min. :-1.8203
## 1st Qu.:-0.7409
## Median :-0.1403
## Mean : 0.0000
## 3rd Qu.: 0.6127
## Max. : 3.1850Now, let’s perform PCA for the standerdized data
#perform principal component analysis (with the SVD method)
pca_humanW2 <- prcomp(humanW_std)
# draw a biplot of the principal component representation and the original variables
biplot(pca_humanW2, choices = 1:2, cex = c(0.8, 1), col = c("grey55", "deeppink4"))
from the previous plots we can see that Maternal mortality ratio and Adolescent birth rate are contributing most to the PC1 with strong positive correlation with each other; meanwhile, they are quite negatively correlated to Expected years of schooling, Life expectancy at birth and Proportion of females with at least secondary education. However, all previous variables are very weakly correlated to * Proportion of females in the labour force* and Percetange of female representatives in parliament which are (the later) contributing more to the PC2. Such interpretation goes well with the former correlation matrix and is not feasible in the first biplot without standerdizing the variables for comparison.
Analysing the first two principal component dimensions of the biplot
s <- summary(pca_humanW2)
# rounded percetanges of variance captured by each PC
pca_pr <- round(100*s$importance[2, ], digits = 1)
# print out the percentages of variance
pca_pr## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
## 51.7 15.5 12.2 9.1 3.8 3.5 2.6 1.5# create object pc_lab to be used as axis labels
paste0(names(pca_pr), " (", pca_pr, "%)")## [1] "PC1 (51.7%)" "PC2 (15.5%)" "PC3 (12.2%)" "PC4 (9.1%)" "PC5 (3.8%)"
## [6] "PC6 (3.5%)" "PC7 (2.6%)" "PC8 (1.5%)"pc_lab <- paste0(names(pca_pr), " (", pca_pr, "%)")
pc_lab## [1] "PC1 (51.7%)" "PC2 (15.5%)" "PC3 (12.2%)" "PC4 (9.1%)" "PC5 (3.8%)"
## [6] "PC6 (3.5%)" "PC7 (2.6%)" "PC8 (1.5%)"# draw a biplot
biplot(pca_humanW2, cex = c(0.8, 1), col = c("grey60", "deeppink2"), xlab = pc_lab[1], ylab = pc_lab[2])
Here we can see that most of the variation is accounted for by the first two principal components which indicates validity of analysis. As we referred earlier Maternal mortality ratio and Adolescent birth rate are the most important variables which are found to be highly predicting less educational oppurtunities and shorter life span of related subjects. However, * Proportion of females in the labour force* and Percetange of female representatives in parliament seem to be related to other players which are not among our study variables.
The tea dataset
library(FactoMineR)## Warning: package 'FactoMineR' was built under R version 3.4.3library(tidyr)
data(tea)
str(tea)## 'data.frame': 300 obs. of 36 variables:
## $ breakfast : Factor w/ 2 levels "breakfast","Not.breakfast": 1 1 2 2 1 2 1 2 1 1 ...
## $ tea.time : Factor w/ 2 levels "Not.tea time",..: 1 1 2 1 1 1 2 2 2 1 ...
## $ evening : Factor w/ 2 levels "evening","Not.evening": 2 2 1 2 1 2 2 1 2 1 ...
## $ lunch : Factor w/ 2 levels "lunch","Not.lunch": 2 2 2 2 2 2 2 2 2 2 ...
## $ dinner : Factor w/ 2 levels "dinner","Not.dinner": 2 2 1 1 2 1 2 2 2 2 ...
## $ always : Factor w/ 2 levels "always","Not.always": 2 2 2 2 1 2 2 2 2 2 ...
## $ home : Factor w/ 2 levels "home","Not.home": 1 1 1 1 1 1 1 1 1 1 ...
## $ work : Factor w/ 2 levels "Not.work","work": 1 1 2 1 1 1 1 1 1 1 ...
## $ tearoom : Factor w/ 2 levels "Not.tearoom",..: 1 1 1 1 1 1 1 1 1 2 ...
## $ friends : Factor w/ 2 levels "friends","Not.friends": 2 2 1 2 2 2 1 2 2 2 ...
## $ resto : Factor w/ 2 levels "Not.resto","resto": 1 1 2 1 1 1 1 1 1 1 ...
## $ pub : Factor w/ 2 levels "Not.pub","pub": 1 1 1 1 1 1 1 1 1 1 ...
## $ Tea : Factor w/ 3 levels "black","Earl Grey",..: 1 1 2 2 2 2 2 1 2 1 ...
## $ How : Factor w/ 4 levels "alone","lemon",..: 1 3 1 1 1 1 1 3 3 1 ...
## $ sugar : Factor w/ 2 levels "No.sugar","sugar": 2 1 1 2 1 1 1 1 1 1 ...
## $ how : Factor w/ 3 levels "tea bag","tea bag+unpackaged",..: 1 1 1 1 1 1 1 1 2 2 ...
## $ where : Factor w/ 3 levels "chain store",..: 1 1 1 1 1 1 1 1 2 2 ...
## $ price : Factor w/ 6 levels "p_branded","p_cheap",..: 4 6 6 6 6 3 6 6 5 5 ...
## $ age : int 39 45 47 23 48 21 37 36 40 37 ...
## $ sex : Factor w/ 2 levels "F","M": 2 1 1 2 2 2 2 1 2 2 ...
## $ SPC : Factor w/ 7 levels "employee","middle",..: 2 2 4 6 1 6 5 2 5 5 ...
## $ Sport : Factor w/ 2 levels "Not.sportsman",..: 2 2 2 1 2 2 2 2 2 1 ...
## $ age_Q : Factor w/ 5 levels "15-24","25-34",..: 3 4 4 1 4 1 3 3 3 3 ...
## $ frequency : Factor w/ 4 levels "1/day","1 to 2/week",..: 1 1 3 1 3 1 4 2 3 3 ...
## $ escape.exoticism: Factor w/ 2 levels "escape-exoticism",..: 2 1 2 1 1 2 2 2 2 2 ...
## $ spirituality : Factor w/ 2 levels "Not.spirituality",..: 1 1 1 2 2 1 1 1 1 1 ...
## $ healthy : Factor w/ 2 levels "healthy","Not.healthy": 1 1 1 1 2 1 1 1 2 1 ...
## $ diuretic : Factor w/ 2 levels "diuretic","Not.diuretic": 2 1 1 2 1 2 2 2 2 1 ...
## $ friendliness : Factor w/ 2 levels "friendliness",..: 2 2 1 2 1 2 2 1 2 1 ...
## $ iron.absorption : Factor w/ 2 levels "iron absorption",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ feminine : Factor w/ 2 levels "feminine","Not.feminine": 2 2 2 2 2 2 2 1 2 2 ...
## $ sophisticated : Factor w/ 2 levels "Not.sophisticated",..: 1 1 1 2 1 1 1 2 2 1 ...
## $ slimming : Factor w/ 2 levels "No.slimming",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ exciting : Factor w/ 2 levels "exciting","No.exciting": 2 1 2 2 2 2 2 2 2 2 ...
## $ relaxing : Factor w/ 2 levels "No.relaxing",..: 1 1 2 2 2 2 2 2 2 2 ...
## $ effect.on.health: Factor w/ 2 levels "effect on health",..: 2 2 2 2 2 2 2 2 2 2 ...dim(tea)## [1] 300 36keep_ <- c("How", "how", "sugar", "where", "lunch", "healthy", "diuretic")
teaW <- dplyr::select(tea, one_of(keep_))
gather(teaW) %>% ggplot(aes(value)) + facet_wrap("key", scales = "free") + geom_bar() + theme(axis.text.x = element_text(angle = 45, hjust = 1, size = 8))## Warning: attributes are not identical across measure variables;
## they will be dropped
then, let’s do Multiple Correspondence Analysis on the tea data
# multiple correspondence analysis
mca <- MCA(teaW, graph = FALSE)
# summary of the model
summary(mca)##
## Call:
## MCA(X = teaW, graph = FALSE)
##
##
## Eigenvalues
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6
## Variance 0.235 0.221 0.185 0.162 0.158 0.134
## % of var. 14.944 14.076 11.802 10.327 10.047 8.538
## Cumulative % of var. 14.944 29.020 40.822 51.149 61.196 69.734
## Dim.7 Dim.8 Dim.9 Dim.10 Dim.11
## Variance 0.123 0.116 0.101 0.079 0.057
## % of var. 7.837 7.402 6.396 5.026 3.606
## Cumulative % of var. 77.571 84.973 91.369 96.394 100.000
##
## Individuals (the 10 first)
## Dim.1 ctr cos2 Dim.2 ctr cos2 Dim.3
## 1 | -0.537 0.409 0.410 | -0.234 0.082 0.078 | 0.177
## 2 | -0.354 0.178 0.119 | 0.167 0.042 0.026 | -0.593
## 3 | -0.311 0.137 0.164 | -0.029 0.001 0.001 | -0.617
## 4 | -0.537 0.409 0.410 | -0.234 0.082 0.078 | 0.177
## 5 | -0.356 0.179 0.147 | -0.212 0.068 0.052 | -0.263
## 6 | -0.413 0.242 0.250 | -0.153 0.035 0.034 | -0.196
## 7 | -0.413 0.242 0.250 | -0.153 0.035 0.034 | -0.196
## 8 | -0.456 0.295 0.182 | 0.043 0.003 0.002 | -0.172
## 9 | 0.315 0.141 0.051 | 0.516 0.400 0.137 | 0.543
## 10 | 0.504 0.361 0.227 | 0.626 0.591 0.350 | -0.256
## ctr cos2
## 1 0.057 0.045 |
## 2 0.632 0.335 |
## 3 0.684 0.646 |
## 4 0.057 0.045 |
## 5 0.124 0.080 |
## 6 0.069 0.056 |
## 7 0.069 0.056 |
## 8 0.053 0.026 |
## 9 0.531 0.152 |
## 10 0.118 0.058 |
##
## Categories (the 10 first)
## Dim.1 ctr cos2 v.test Dim.2 ctr
## alone | -0.102 0.409 0.019 -2.397 | -0.232 2.254
## lemon | 0.928 5.768 0.107 5.644 | 0.009 0.001
## milk | -0.247 0.776 0.016 -2.198 | 0.414 2.319
## other | 0.525 0.504 0.009 1.597 | 2.094 8.496
## tea bag | -0.676 15.743 0.597 -13.363 | -0.121 0.534
## tea bag+unpackaged | 0.622 7.369 0.176 7.263 | 0.850 14.636
## unpackaged | 1.568 17.941 0.335 10.010 | -1.650 21.100
## No.sugar | 0.203 1.292 0.044 3.625 | 0.130 0.561
## sugar | -0.217 1.381 0.044 -3.625 | -0.139 0.599
## chain store | -0.623 15.120 0.690 -14.368 | -0.145 0.865
## cos2 v.test Dim.3 ctr cos2 v.test
## alone 0.100 -5.461 | -0.079 0.315 0.012 -1.868 |
## lemon 0.000 0.053 | 0.855 6.188 0.090 5.195 |
## milk 0.045 3.687 | -0.007 0.001 0.000 -0.062 |
## other 0.136 6.368 | -1.367 4.317 0.058 -4.156 |
## tea bag 0.019 -2.389 | -0.173 1.308 0.039 -3.424 |
## tea bag+unpackaged 0.330 9.934 | 0.436 4.594 0.087 5.096 |
## unpackaged 0.371 -10.536 | -0.322 0.956 0.014 -2.054 |
## No.sugar 0.018 2.317 | -0.544 11.799 0.317 -9.734 |
## sugar 0.018 -2.317 | 0.582 12.613 0.317 9.734 |
## chain store 0.037 -3.335 | -0.103 0.524 0.019 -2.378 |
##
## Categorical variables (eta2)
## Dim.1 Dim.2 Dim.3
## How | 0.123 0.202 0.140 |
## how | 0.675 0.562 0.089 |
## sugar | 0.044 0.018 0.317 |
## where | 0.755 0.613 0.054 |
## lunch | 0.013 0.037 0.066 |
## healthy | 0.005 0.076 0.240 |
## diuretic | 0.029 0.040 0.392 |# visualize MCA
plot(mca, invisible=c("ind"),habillage = "quali" )
here for example we can see that drinking unpackaged tea is more similar to drinking tea in tea shops, as well as, drinking tea in both chain stores and tea shops is more related to drinking both bagged and unpackaged tea category.